DEDUCTIVE LOGIC
HORACE HART, PRINTER TO THE UNIVERSITY
DEDUCTIVE LOGIC
EY
ST. GEORGE STOCK, M.A.
PEMBROKE COLLEGE, OXFORD
Bon&on
LONGMANS, GREEN, AND CO.
1888
[ All rights reserved ]
PREFACE.
ONE critic, who was kind enough to look at this book
in manuscript, recommended me to abandon the design
of publishing it, on the ground that my logic was too
like all other logics ; another suggested to me to cut out
a considerable amount of new matter. The latter advice
I have followed ; the former has encouraged me to hope
that I shall not be considered guilty of wanton innovation.
The few novelties which I have ventured to retain will, I
trust, be regarded as legitimate extensions of received
lines of teaching. }
My object has been to produce a work which should
be as thoroughly representative of the present state of the
logic of the Oxford Schools as any of the text-books of
the past. The qualities which I have aimed at before all
others have been clearness and consistency. For the
task which I have taken upon myself I may claim one
qualification — that of experience ; since more than seven
teen years have now elapsed since I took my first pupil
in logic for the Honour School of Moderations, and
during that time I have been pretty continuously engaged
in studying and teaching the subject.
a 3
vi PREFACE.
In acknowledging my obligations to previous writers
I must begin with Archbishop Whately, whose writings
first gave me an interest in the subject. The works of
Mill and Hamilton have of course been freely drawn
upon. I have not followed either of those two great
writers exclusively, but have endeavoured to assimilate
what seemed best in both. To Professor Fowler I am
under a special debt. I had not the privilege of personal
teaching from him in logic, as I had in some other sub
jects ; but his book fell into my hands at an early period
in my mental training, and was so thoroughly studied as
to have become a permanent part of the furniture of my
mind. Much the same may be said of my relation to the
late Professor Jevons's Elementary Lessons in Logic.
Two other books, which I feel bound to mention with
special emphasis, are Mansel's edition of Aldrich and
McCosh's Laws of Discursive Thought. If there be
added to the foregoing Watts' s Logic, Thomson's Outlines
of the Laws of Thought, Bain's Deductive Logic, Jevons's
Studies in Deductive Logic and Principles of Science,
Bradley's Principles of Logic, Abbott's Elements of Logic,
Walker's edition of Murray, Ray's Text-book of Deduc
tive Logic, and Weatherley's Rudiments of Logic, I think
the list will be exhausted of modern works from which I
am conscious of having borrowed. But, not to forget
the sun, while thanking the manufacturers of lamps and
candles, I should add that I have studied the works of
PREFACE. vil
Aristotle according to the measure of my time and
ability.
This work has had the great advantage of having been
revised, while still in manuscript, by Mr. Alfred Robinson,
Fellow of New College, to whom I cannot sufficiently ex
press my obligation. I have availed myself to the full of
the series of criticisms which he was kind enough to send
me. As some additions have been made since then, he
cannot be held in any way responsible for the faults which
less kindly critics may detect.
For the examples at the end I am mainly indebted to
others, and to a large extent to my ingenious friend, the
Rev. W. J. Priest of Merlon College.
My thanks are due also to my friend and former pupil,
Mr. Gilbert Grindle, Scholar of Corpus, who has been at
the pains to compose an index, and to revise the proofs
as they passed through the press.
And last, but not least, I must set on record my
gratitude to Commander R. A. Stock, R.N., one of Her
Majesty's Knights of Windsor, without whose brotherly
aid this work might never have been written, and would
certainly not have assumed exactly its present shape.
OXFORD,
October 22, 1888.
CONTENTS.
PREFACE v-vii
INTRODUCTION, §§ 1-56 . . . . . • . . 1-14
PART!. Of Terms, §§ 57-171 . . • 15-50
CHAP. I. Of the Term as distinguished from other
Words, §§ 57-76 . . . . 15
II. Of the Division of Things, §§ 77-85 . . 20
III. Of the Divisions of Terms, §§ 86-165 . 23
IV. Of the Law of Inverse Variation of Exten
sion and Intension, §§ 166-171 . 48
PART II. Of Propositions, §§ 172-425 . ' .' . . 51-125
CHAP. I. Of the Proposition as distinguished from
other Sentences, §§ 172-185 . ' . 51
II. Of the Copula, §§ 186-201 ' '. . .- . 54
III. Of the Divisions of Propositions, §§ 202-
273. . . . . . . 59
IV. Of the Distribution of Terms, §§ 274-294 . 76
V. Of the Quantification of the Predicate,
§§ 295-312 ....'... 82
VI. Of the Heads of Predicables, §§ 313-346 . 87
VII. Of Definition, §§ 347-384. ... 99
VIII. Of Division, §§ 385-425 . . . . 115
X CONTENTS.
PAGES
PART III. Of Inferences, §§ 426-884 . . 126-317
CHAP. I. Of Inferences in general, §§ 426-441 126
II. Of Deductive Inferences, §§ 442-448 133
III. Of Opposition, §§ 449-478 . . .' 135
IV. Of Conversion, §§ 479-495 ... 143
V. Of Permutation, §§ 496-502 ... 148
VI. Of Compound Forms of Immediate infer
ence, §§ 503-532 . . '. . 151
VII. Of Other Forms of Immediate Inference,
§§ 533-539 ..... 161
VIII. Of Mediate Inferences or Syllogisms,
§§ 540-557 . . ...... 164
. IX. Of Mood and Figure, §§ 558-568 . . 169
X. Of the Canon of Reasoning, §§ 569-581 . 174
XI. Of the General Rules of Syllogism, §§ 582-
598 . . . ' 178
XII. Of the Determination of the Legitimate
Moods of Syllogism, §§ 599-605 . 186
XIII. Of the Special Rules of the Four Figures,
§§ 606-620 . . . . 189
XIV. Of the Determination of the Moods that are
valid in the Four Figures, §§ 621-632 194
XV. Of the Special Canons of the Four Figures,
§§ 633-647 ..... 199
XVI. Of the Special Uses of the Four Figures,
§§ 648-655 . . . 214
XVII. Of the Syllogism with Three Figures,
§§ 656-666 . . ,. '. - . 117
XVIII. Of Reduction, §§ 667-700. ... 222
CONTENTS. xi
PAGES
CHAP. XIX. Of Immediate Inference as applied to
Complex Propositions, §§ 701-730 . 234
XX. Of Complex Syllogisms, §§ 731-743 . .. 246
XXI. Of the Reduction of the Partly Conjunctive
Syllogism, §§ 744-752 . . . 251
XXII. Of the Partly Conjunctive Syllogism re
garded as an Immediate Inference,
§§ 753-759 . . . -. . ; 256
XXIII. Of the Disjunctive Syllogism, §§ 760-765 . 259
XXIV. Of the Reduction of the Disjunctive Syllo
gism, §§ 766-769 .... 262
XXV. Of the Disjunctive Syllogism regarded as an
Immediate Inference, §§ 770-777 . 265
XXVI. Of the Mixed Form of Complex Syllogism,
§§ 778-795 268
XXVII. Of the Reduction of the Dilemma, §§ 796-
797. . - . . . . . 278
XXVIII. Of the Dilemma regarded as an Immediate
Inference, §§ 798, 799 . . . 280
XXIX. Of Trains of Reasoning, §§ 800-826 . '. 282
XXX. Of Fallacies, §§ 827-884 . . . 294
EXERCISES . .'....<. . . . . 319-349
INDEX . . ....... . . 35*-35<5
INTRODUCTION.
§ 1. LOGIC is divided into two branches, namely —
(1) Inductive,
(2) Deductive.
§ 2. The problem of inductive logic is to determine the
actual truth or falsity of propositions : the problem of
deductive logic is to determine their relative truth or
falsity, that is to say, given such and such propositions as
true, what others will follow from them.
§ 3. Hence in the natural order of treatment inductive
logic precedes deductive, since it is induction which sup
plies us with the general truths, from which we reason
down in our deductive inferences.
§ 4. It is not, however, with logic as a whole that we
are here concerned, but only with deductive logic, which
may be denned as The Science of the Formal Laws of
Thought.
§ 5. In order fully to understand this definition we must
know exactly what is meant by ' thought,' by a ' law of
thought/ by the term ' formal,' and by ' science.'
§ 6. Thought, as here used, is confined to the faculty of
comparison. All thought involves comparison, that is to
say, a recognition of likeness or unlikeness.
B
2 INTRODUCTION.
§ 7. The laws of thought are the conditions of correct
thinking. The term ' law/ however, is so ambiguous that
it will be well to determine more precisely in what sense it
is here used.
§ 8. We talk of the ' laws of the land ' and of the ' laws
of nature/ and it is evident that we mean very different
things by these expressions. By a law in the political
sense is meant a command imposed by a superior upon an
inferior and sanctioned by a penalty for disobedience.
But by the ' laws of nature ' are meant merely certain
uniformities among natural phenomena ; for instance, the
' law of gravitation ' means that every particle of matter
does invariably attract every other particle of matter in the
universe.
§ 9. The word ' law ' is transferred by a metaphor from
one of these senses to the other. The effect of such a
command as that described above is to produce a certain
amount of uniformity in the conduct of men, and so, where
we observe uniformity in nature, we assume that it is the
result of such a command, whereas the only thing really
known to us is the fact of uniformity itself.
§ 10. Now in which of these two senses are we using
the term ' laws of thought ' ? The laws of the land, it is
plain, are often violated, whereas the laws of nature never
can be so l. Can the laws of thought be violated in like
1 There is a sense in which people frequently speak of the laws of
nature being violated, as when one says that intemperance or celibacy
is a violation of the laws of nature, but here by 'nature ' is meant an
ideal perfection in the conditions of existence.
INTR OD UC TION. 3
manner with the laws of the land ? Or are they inviolable
like the laws of nature ?
§ 11. In appearance they can be, and manifestly often
are violated — for how else could error be possible ? But
in reality they can not. No man ever accepts a contradic
tion when it presents itself to the mind as such : but when
reasoning is at all complicated what does really involve
a contradiction is not seen to do so ; and this sort of error
is further assisted by the infinite perplexities of language.
§ 12. The laws of thought then in their ultimate expres
sion are certain uniformities which invariably hold among
mental phenomena, and so far they resemble the laws of
nature: but in their complex applications they may be
violated owing to error, as the laws of the land may be
violated by crime.
§ 13. We have now to determine the meaning of the
expression ' formal laws of thought/
§ 14. The distinction between form and matter is one
which pervades all nature. We are familiar with it in the
case of concrete things. A cup, for instance, with pre
cisely the same form, may be composed of very different
matter — gold, silver, pewter, horn or what not ?
§ 1 5. Similarly in every act of thought we may distin
guish two things —
(1) the object thought about,
(2) the way in which the mind thinks of it.
The first is called the Matter ; the second the Form of
Thought.
§ 16. Now Formal, which is another name for Deduc-
B 2
4 INTRODUCTION.
tive Logic, is concerned only with the way in which the
mind thinks, and has nothing to do with the particular
objects thought about.
§17. Since the form may be the same, whilst the matter
is different, we may say that formal logic is concerned
with the essential and necessary elements of thought as
opposed to such as are accidental and contingent. By
' contingent ' is meant what holds true in some cases, but
not in others. For instance, in the particular case of
equilateral triangles it is true to say, not only that ' all
equilateral triangles are equiangular,' but also that ' all
equiangular triangles are equilateral.' But the evidence for
these two propositions is independent. The one is not
a formal consequence of the other. If it were, we should
be able to apply the same inference to all matter, and
assert generally that if all A is B, all B is A, which it is
notorious that we cannot do.
§ 18. It remains now for the full elucidation of our
definition to determine what is meant by ' science.'
§ 19. The question has often been discussed whether
logic is a science or an art. The answer to it must
depend upon the meaning we assign to these terms.
§20. Broadly speaking, there is the same difference
between Science and Art as there is between knowing and
doing.
Science is systematized knowledge ;
Art is systematized action.
Science is acquired by study ;
Art is acquired by practice.
INTRODUCTION. 5
§ 21. Now logic is manifestly a branch of knowledge,
and does not necessarily confer any practical skill. It is
only the right use of its rules in thinking which can make
men think better. It is therefore, in the broad sense of
the terms, wholly a science and not at all an art.
§ 22. But this word ' art/ like most others, is ambiguous,
and is often used, not for skill displayed in practice, but
for the knowledge necessary thereto. This meaning is
better conveyed by the term ' practical science/
§ 23. Science is either speculative or practical. In the
first case we study merely that we may know; in the
latter that we may do.
Anatomy is a speculative science ;
Surgery is a practical science.
In the first case we study the human frame in order
that we may understand its structure ; in the second that
we may assist its needs. Whether logic is a speculative
or a practical science depends entirely upon the way in
which it is treated. If we study the laws of thought
merely that we may know what they are, we are making
it a speculative science ; if we study the same laws with
a view to deducing rules for the guidance of thought, we
are making it a practical science.
§ 24. Hence logic may be declared to be both the
science and the art of thinking. It is the art of thinking
in the same sense in which grammar is the art of speaking.
Grammar is not in itself the right use of words, but
a knowledge of it enables men to use words correctly. In
the same way a knowledge of logic enables men to think
6 INTR OD UCTION.
correctly, or at least to avoid incorrect thoughts. As an
art logic may be called the navigation of the sea of
thought.
§ 25. The laws of thought are all reducible to the
three following axioms, which are known as The Three
Fundamental Laws of Thought.
1 i ) The Law of Identity —
Whatever is, is ;
or, in a more precise form,
Every A is A.
(2) The Law of Contradiction —
Nothing can both be and not be ;
Nothing can be A and not A.
(3) The Law of Excluded Middle—
Everything must either be or not be ;
Everything is either A or not A.
§ 26. Each of these principles is independent and self-
evident.
§ 27. If it were possible for the law of identity to be
violated, no violation of the law of contradiction would
necessarily ensue : for a thing might then be something
else, without being itself at the same time, which latter is
what the law of contradiction militates against. Neither
would the law of excluded middle be infringed. For, on
the supposition, a thing would be something else, whereas
all that the law of excluded middle demands is that
it should either be itself or not. A would in this case
adopt the alternative of being not A.
§ 28. Again, the violation of the law of contradiction
INTRODUCTION. 7
does not involve any violation of the law of identity : for
a thing might in that case be still itself, so that the law of
identity would be observed, even though, owing to the
law of contradiction not holding, it were not itself at the
same time. Neither would the law of excluded middle
be infringed. For a thing would, on the supposition, be
both itself and not itself, which is the very reverse of
being neither.
§ 29. Lastly, the law of excluded middle might be
violated without a violation of the law of contradiction :
for we should then have a thing which was neither A nor
not A, but not a thing which was both at the same time.
Neither would the law of identity be infringed. For we
should in this case have a thing which neither was nor was
not, so that the conditions of the law of identity could not
exist to be broken. That law postulates that whatever is,
is : here we have a thing which never was to begin with.
§ 30. These principles are of so simple a character that
the discussion of them is apt to be regarded as puerile.
Especially is this the case with regard to the law of
identity. This principle in fact is one of those things
which are 'more honoured in the breach than in the
observance.' Suppose for a moment that this law did
not hold — then what would become of all our reasoning ?
Where would be the use of establishing conclusions about
things, if they were liable to evade us by a Protean change
of identity ?
§ 31. The remaining two laws supplement each other
in the following way. The law of contradiction enables
8 INTRODUCTION.
us to affirm of two exhaustive and mutually exclusive
alternatives, that it is impossible for both to be true ; the
law of excluded middle entitles us to add, that it is equally
impossible for both to be false. Or, to put the same
thing in a different form, the law of contradiction lays
down that one of two such alternatives must be false ; the
law of excluded middle adds that one must be true.
§ 32. There are three processes of thought —
(1) Conception.
(2) Judgement.
(3) Inference or Reasoning.
§ 33. Conception, which is otherwise known as Simple
Apprehension, is the act of forming in the mind the idea
of anything, e. g. when we form in the mind the idea of a
cup, we are performing the process of conception.
§ 34. Judgement, in the sense in which it is here used1,
may be resolved into putting two ideas together in the
mind, and pronouncing as to their agreement or disagree
ment, e. g. we have in our minds the idea of a cup and the
idea of a thing made of porcelain, and we combine them
in the judgement — ' This cup is made of porcelain/
§ 35. Inference, or Reasoning, is the passage of the
mind from one or more judgements to another, e. g. from
the two judgements ' Whatever is made of porcelain is
brittle,' and ' This cup is made of porcelain/ we elicit a
third judgement, ' This cup is brittle/
1 Sometimes the term ' judgement ' is extended to the comparison
of nameless sense-impressions, which underlies the formation of con
cepts. But this amounts to identifying judgement with thought in
general.
INTRODUCTION. 9
§ 36. Corresponding to these three processes there are
three products of thought, viz.
(1) The Concept.
(2) The Judgement.
(3) The Inference.
§ 37. Since our language has a tendency to confuse
the distinction between processes and products *, it is the
more necessary to keep them distinct in thought. Strictly
we ought to speak of conceiving, judging and inferring
on the one hand, and, on the other, of the concept, the
judgement and the inference.
The direct object of logic is the study of the products
rather than of the processes of thought. But, at the same
time, in studying the products we are studying the pro
cesses in the only way in which it is possible to do so.
For the human mind cannot be both actor and spectator
at once ; we must wait until a thought is formed in our
minds before we can examine it. Thought must be
already dead in order to be dissected : there is no vivi
section of consciousness. Thus we can never know
more of the processes of thought than what is revealed to
us in their products.
§ 38. When the three products of thought are expressed
in language, they are called respectively
(1) The Term.
(2) The Proposition.
(3) The Inference.
1 E. g. We have to speak quite indiscriminately of Sensation,
Imagination, Reflexion, Sight, Thought, Division, Definition, and so
on, whether we mean in any case a process or a product.
10 INTRODUCTION.
§ 39. Such is the ambiguity of language that we have
already used the term * inference ' in three different
senses — first, for the act or process of inferring ; secondly,
for the result of that act as it exists in the mind ; and,
thirdly, for the same thing as expressed in language.
Later on we shall have to notice a further ambiguity in
its use.
§ 40. It has been declared that thought in general is
the faculty of comparison, and we have now seen that
there are three products of thought. It follows that each
of these products of thought must be the result of a com
parison of some kind or other.
The concept is the result of comparing attributes.
The judgement is the result of comparing concepts.
The inference is the result of comparing judgements.
§ 41. In what follows we shall, for convenience, adopt
the phraseology which regards the products of thought as
clothed in language in preference to that which regards
the same products as they exist in the mind of the
individual. For although the object of logic is to examine
thought pure and simple, it is obviously impossible to
discuss it except as clothed in language. Accordingly
the three statements above made may be expressed as
follows —
The term is the result of comparing attributes.
The proposition is the result of comparing terms.
The inference is the result of comparing propositions.
§ 42. There is an advantage attending the change of
language in the fact that the word ' concept ' is not an
INTR OD UCTION. 1 J
adequate expression for the first of the three products of
thought, whereas the word ' term ' is. By a concept is
meant a general notion, or the idea of a class, which
corresponds only to a common term. Now not only are
common terms the results of comparison, but singular
terms, or the names of individuals, are so too.
§ 43. The earliest result of thought is the recogni
tion of an individual object as such, that is to say as
distinguished and marked off from the mass of its
surroundings. No doubt the first impression produced
upon the nascent intelligence of an infant is that of a
confused whole. It requires much exercise of thought to
distinguish this whole into its parts. The completeness of
the recognition of an individual object is announced by
attaching a name to it. Hence even an individual name,
or singular term, implies thought or comparison. Before
the child can attach a meaning to the word * mother/
which to it is a' singular term, it must have distinguished
between the set of impressions produced in it by one
object from those which are produced in it by others.
Thus, when Vergil says
Incipe, parve puer, risu cognoscere matrem,
he is exhorting the beatific infant to the exercise of the
faculty of comparison.
§ 44. That a common term implies comparison does
not need to be insisted upon. It is because things
resemble each other in certain of their attributes that we
call them by a common name, and this resemblance could
1 2 2NTR OD UCTION.
not be ascertained except by comparison, at some time
and by some one. Thus a common term, or concept, is
the compressed result of an indefinite number of compari
sons, which lie wrapped up in it like so many fossils,
witnessing to prior ages of thought.
§ 45. In the next product of thought, namely, the pro
position, we have the result of a single act of comparison
between two terms; and this is why the proposition is
called the unit of thought, as being the simplest and most
direct result of comparison.
§ 46. In the third product of thought, namely, the
inference, we have a comparison of propositions either
directly or by means of a third. This will be explained
later on. For the present we return to the first product
of thought.
§ 47. The nature of singular terms has not given rise
to much dispute; but the nature of common terms has
been the great battle-ground of logicians. What cor
responds to a singular term is easy to determine, for the
thing of which it is a name is there to point to : but the
meaning of a common term, like ' man ' or ' horse,' is
not so obvious as people are apt to think on first hearing
of the question.
§ 48. A common term or class-name was known to
mediaeval logicians under the title of a Universal ; and it
was on the question ' What is a Universal ? ' that they
split into the three schools of Realists, Nominalists, and
Conceptualists. Here are the answers of the three
schools to this question in their most exaggerated form —
INTRODUCTION. 13
§ 49. Universals, said the Realists, are substances
having an independent existence in nature.
§ 50. Universals, said the Nominalists, are a mere
matter of words, the members of what we call a class
having nothing in common but the name.
§ 51. Universals, said the Conceptualists, exist in the
mind alone. They are the conceptions under which the
mind regards external objects.
§ 52. The origin of pure Realism is due to Plato and
his doctrine of ' ideas ' ; for Idealism, in this sense, is not
opposed to Realism, but identical with it. Plato seems to
have imagined that, as there was a really existing thing
corresponding to a singular term, such as Socrates, so
there must be a really existing thing corresponding to the
common term ' man.' But when once the existence of
these general objects is admitted, they swamp all other
existences. For individual men are fleeting and transitory
— subject to growth, decay and death — whereas the idea
of man is imperishable and eternal. It is only by
partaking in the nature of these ideas that individual
objects exist at all.
§ 53. Pure Nominalism was the swing of the pendulum
of thought to the very opposite extreme ; while Conceptu-
alism was an attempt to hit the happy mean between the
two.
§ 54. Roughly it may be said that the Realists sought
for the answer to the question ' What is a Universal ? ' in
the matter of thought, the Conceptualists in the form, and
the Nominalists in the expression.
14 INTRODUCTION.
§ 55. A full answer to the question ' What is a
Universal ? ' will bring in something of the three views
above given, while avoiding the exaggeration of each. A
Universal is a number of things that are called by the
same name ; but they would not be called by the same
name unless they fell under the same conception in the
mind ; nor would they fall under the same conception in
the mind unless there actually existed similar attributes in
the several members of a class, causing us to regard them
under the same conception and to give them the same
name. Universals therefore do exist in nature, and not
merely in the mind of man : but their existence is depen
dent upon individual objects, instead of individual objects
depending for their existence upon them. Aristotle saw
this very clearly, and marked the distinction between the
objects corresponding to the singular and to the common
term by calling the former Primary and the latter Second
ary Existences. Rosinante and Excalibur are primary,
but * horse ' and ' sword ' secondary existences.
§ 56. We have seen that the three products of thought
are each one stage in advance of the other, the inference
being built upon the proposition, as the proposition is
built upon the term. Logic therefore naturally divides
itself into three parts.
The First Part of Logic deals with the Term ;
The Second Part deals with the Proposition ;
The Third Part deals with the Inference.
PART I.— OF TERMS.
CHAPTER I.
Of the Term as distinguished from other words.
§ 57. The word 'term' means a boundary.
§ 58. The subject and predicate are the two terms, or
boundaries, of a proposition. In a proposition we start
from a subject and end in a predicate (§§ 182-4), there
being nothing intermediate between the two except the
act of pronouncing as to their agreement or disagreement,
which is registered externally under the sign of the copula.
Thus the subject is the ' terminus a quo/ and the predicate
is the ' terminus ad quern.'
§ 59. Hence it appears that the term by its very name
indicates that it is arrived at by an analysis of the proposi
tion. It is the judgement or proposition that is the true
unit of thought and speech. The proposition as a whole
is prior in conception to the terms which are its parts:
but the parts must come before the whole in the synthetic,
order of treatment.
§ 60. A term is the same thing as a name or noun.
§ 61. A name is a word, or collection of words, which
serves as a mark to recall or transmit the idea of a thing,
either in itself or through some of its attributes.
1 6 OF THE TERM AS DISTINGUISHED
§ 62. Nouns, or names, are either Substantive or Adjec
tive.
A Noun Substantive is the name of a thing in itself,
that is to say, without reference to any special attribute.
§ 63. A Noun Adjective is a name which we are
entitled to add to a thing, when we know it to possess a
given attribute.
§ 64. The Verb, as such, is not recognised by logic, but
is resolved into predicate and copula, that is to say, into
a noun which is affirmed or denied of another, plus the
sign of that affirmation or denial. ' The kettle boils ' is
logically equivalent to ' The kettle is boiling/ though it is
by no means necessary to express the proposition in the
latter shape. Here we see that ' boils ' is equivalent to the
noun ' boiling ' together with the copula ' is,' which declares
its agreement with the noun { kettle/ ' Boiling ' here is a
noun adjective, which we are entitled to add to ' kettle/ in
virtue of certain knowledge which we have about the
latter. Being a verbal noun, it is called in grammar
a participle, rather than a mere adjective. The word
' attributive ' in logic embraces both the adjective and
participle of grammar.
§ 65. In grammar every noun is a separate word : but
to logic, which is concerned with the thought rather than
with the expression, it is indifferent whether a noun, or
term, consists of one word or many. The latter are
known as ' many-worded names/ In the following
passage, taken at random from Butler's Analogy —
' These several observations', concerning the active prin-
FROM OTHER WORDS. 17
ciple of virtue and obedience to God's commands, are
applicable to passive submission or resignation to his
will ' — we find the subject consisting of fourteen words,
and the predicate of nine. It is the exception rather than
the rule to find a predicate which consists of a single word.
Many-worded names in English often consist of clauses
introduced by the conjunction ' that/ as ' That letters
should be written in strict conformity with nature is true';
often also of a grammatical subject with one or more
dependent clauses attached to it, as
' He who fights and runs away,
Will live to fight another day.'
§ 66. Every term then is not a word, since a term may
consist of a collection of words. Neither is every word
a term. ' Over,' for instance, and ' swiftly/ and, generally,
what are called particles in grammar, do not by themselves
constitute terms, though they may be employed along
with other words to make up a term..
§ 67. The notions with which thought deals involve
many subtle relations and require many nice modifications.
Language has instruments, more or less perfect, whereby
such relations and modifications may be expressed. But
these subsidiary aids to expression do not form a notion
which can either have something asserted of it or be
asserted itself of something else.
§ 68. Hence words are divided into three classes —
(1) Categorematic ;
(2) Syncategorematic ;
(3) Acategorematic.
1 8 OF THE TERM AS DISTINGUISHED
§ 69. A Categorematic word is one which can be used
by itself as a term.
§ 70. A Syncategorematic word is one which can help
to form a term.
§ 71. An Acategorematic word is one which can neither
form, nor help to form, a term l.
§ 72. Categorematic literally means ' predicable/
' Horse/ ' swift/ ' galloping ' are Categorematic. Thus
we can say, ' The horse is swift/ or ' The horse is gallop
ing/ Each of these words forms a term by itself, but
' over ' and ' swiftly ' can only help to form a term, as in the
proposition, 'The horse is galloping swiftly over the plain/
§ 73. A term then may be said to be a Categorematic
word or collection of words, that is to say, one which can
be used by itself as a predicate.
§ 74. To entitle a word or collection of words to be
1 Comparatively few of the parts of speech are Categorematic.
Nouns, whether substantive or adjective, including of course pronouns
and participles, are so, but only in their nominative cases, except
when an oblique case is so used as to be equivalent to an attributive.
Verbs also are Categorematic, but only in three of their moods, the
Indicative, the Infinitive, and the Potential. The Imperative and
Optative moods clearly do not convey assertions at all, while the
Subjunctive can only figure as a subordinate member of some asser
tion. We may notice, too, that the relative pronoun, unlike the
rest, is necessarily Syncategorematic, for the same reason as the
subjunctive mood. Of the remaining parts of speech the article,
adverb, preposition, and conjunction can never be anything but Syn
categorematic, while the interjection is acategorematic, like the
vocative case of nouns and the imperative and optative moods of
verbs, which do not enter at all into the form of sentence known as
the proposition.
FROM OTHER WORDS. 19
called a term, it is not necessary that it should be capable
of standing by itself as a subject. Many terms which
can be used as predicates are incapable of being used as
subjects : but every term which can be used as a subject
(with the doubtful exception of proper names) can be
used also as a predicate. The attributives ' swift ' and
' galloping ' are terms, quite as much as the subject
horse/ but they cannot themselves be used as subjects.
§ 75. When an attributive appears to be used as a sub
ject, it is owing to a grammatical ellipse. Thus in Latin
we say ' Boni sapientes sunt/ and in English ' The good
are wise/ because it is sufficiently declared by the in
flexional form in the one case, and by the usage of the
language in the other, that men are signified. It is an
accident of language how far adjectives can be used as
subjects. They cease to be logical attributives the
moment they are so used.
§ 76. There is a sense in which every word may
become categorematic, namely, when it is used simply as
a word, to the neglect of its proper meaning. Thus we
can say — '" Swiftly" is an adverb/ 'Swiftly' in this
sense is really no more than the proper name for a
particular word. This sense is technically known as the
' suppositio materialis ' of a word.
c 2
CHAPTER II.
Of the Division of Things.
§77. BEFORE entering on the divisions of terms it is
necessary to advert for a moment to a division of the
things whereof they are names.
§78. By a 'thing' is meant simply an object of
thought — whatever one can think about.
§ 79. Things are either Substances or Attributes.
Attributes may be sub-divided into Qualities and Rela
tions.
Thing
Substance Attribute
I
Quality Relation
§ 80. A Substance is a thing which can be conceived to
exist by itself. All bodies are material substances. The
soul, as a thinking subject, is an immaterial substance.
§ 81. An Attribute is a thing which depends for its
existence upon a substance, e.g. greenness, hardness,
weight, which cannot be conceived to exist apart from
green, hard, and heavy substances.
OF THE DIVISION OF THINGS. 21
§ 82. A Quality is an attribute which does not require
more than one substance for its existence. The attributes
just mentioned are qualities. There might be greenness,
hardness, and weight, if there were only one green, hard
and heavy substance in the universe.
§ 83. A Relation is an attribute which requires two or
more substances for its existence, e.g. nearness, fatherhood,
introduction.
§ 84. When we say that a substance can be conceived
to exist by itself, what is meant is that it can be conceived
to exist independently of other substances. We do not
mean that substances can be conceived to exist indepen
dently of attributes, nor yet out of relation to a mind per
ceiving them. Substances, so far as we can know them,
are only collections of attributes. When therefore we say
that substances can be conceived to exist by themselves,
whereas attributes are dependent for their existence upon
substances, the real meaning of the assertion reduces itself
to this, that it is only certain collections of attributes which
can be conceived to exist independently ; whereas single
attributes depend for their existence upon others. The
colour, smoothness or solidity of a table cannot be con
ceived apart from the extension, whereas the whole cluster
of attributes which constitutes the table can be conceived
to exist altogether independently of other such clusters.
We can imagine a table to exist, if the whole material
universe were annihilated, and but one mind left to per
ceive it. Apart from mind, however, we cannot imagine
it : since what we call the attributes of a material substance
22 OF THE DIVISION OF THINGS.
are no more than the various modes in which we find our
minds affected.
§ 85. The above division of things belongs rather to the
domain of metaphysics than of logic: but it is the
indispensable basis of the division of terms, to which we
now proceed.
CHAPTER III.
Of the Division of Terms.
§ 86. THE following scheme presents to the eye the
chief divisions of terms.
/Subject- Term
Attributive
Abstract
Concrete
Singular
Common
Positive
Term^ Privative
Negative
Univocal
Equivocal
Absolute
Relative
Connotative
\Non-connotative
Division of terms according to their
place in thought.
according to the kind of thing sig
nified.
according to Quantity in Extension.
> according to Quality.
according to number of meanings.
) according to number of things involved
) in the name.
according to number of quantities.
Subject- term and Attributive.
§ 87. By a Subject-term is meant any term which is
capable of standing by itself as a subject, e.g. 'ribbon/
' horse.'
§ 88. Attributives can only be used as predicates, not as
24 OF THE DIVISION OF TERMS.
subjects, e. g. ' cherry-coloured/ ' galloping.' These can
only be used in conjunction with other words (syncategore-
matically) to make up a subject. Thus we can say
' A cherry-coloured ribbon is becoming/ or ' A galloping
horse is dangerous.'
§ 89. Attributives are contrivances of language whereby
we indicate that a subject has a certain attribute. Thus,
when we say ' This paper is white/ we indicate that the
subject ' paper ' possesses the attribute whiteness. Logic,
however, also recognises as attributives terms which
signify the non-possession of attributes. ' Not-white ' is an
attributive equally with c white.'
§ 90. An Attributive then may be defined as a term
which signifies the possession, or non-possession, of an
attribute by a subject.
§ 91. It must be carefully noticed that attributives are
not names of attributes, but names of the things which
possess the attributes, in virtue of our knowledge that they
possess them. Thus ' white ' is the name of all the things
which possess the attribute whiteness, and 'virtuous' is
a name, not of the abstract quality, virtue, itself, but of the
men and actions which possess it. It is clear that a term
can only properly be said to be a name of those things
whereof it can be predicated. Now, we cannot intelligibly
predicate an attributive of the abstract quality, or qualities,
the possession of which it implies. We cannot, for in
stance, predicate the term ' learned ' of the abstract quality
of learning : but we may predicate it of the individuals,
Varro and Vergil. Attributives, then, are to be regarded
OF THE DIVISION OF TERMS. 2$
as names, not of the attributes which they imply, but of
the things in which those attributes are found.
§ 92. Attributives, however, are names of things in a
less direct way than that in which subject-terms may be
the names of the same things. Attributives are names of
things only in predication, whereas subject-terms are
names of things in or out of predication. The terms
' horse ' and ' Bucephalus ' are names of certain things, in
this case animals, whether we make any statement about
them or not : but the terms ' swift ' and ' fiery ' only
become names of the same things in virtue of being
predicable of them. When we say ' Horses are swift ' or
' Bucephalus was fiery/ the terms ' swift ' and ' fiery '
become names respectively of the same things as ' horse '
and ' Bucephalus/ This function of attributives as names
in a secondary sense is exactly expressed by the gram
matical term 'noun adjective.' An attributive is not
directly the name of anything. It is a name added on in
virtue of the possession by a given thing of a certain
attribute, or, in some cases, the non-possession.
§ 93. Although attributives cannot be used as subjects,
there is nothing to prevent a subject-term from being used
as a predicate, and so assuming for the time being the
functions of an attributive. When we say ' Socrates was
a man,' we convey to the mind the idea of the same
attributes which are implied by the attributive ' human.'
But those terms only are called attributives which can
never be used except as predicates.
§ 94. This division into Subject-terms and Attributives
26 OF THE DIVISION OF TERMS.
may be regarded as a division of terms according to their
place in thought. Attributives, as we have seen, are
essentially predicates, and can only be thought of in
relation to the subject, whereas the subject is thought of
for its own sake
Abstract and Concrete Terms.
§ 95. An Abstract Term is the name of an attribute,
e. g. whiteness \ multiplication, act, purpose, explosion.
§ 96. A Concrete Term is the name of a substance,
e. g. a man, this chair, the soul, God.
§ 97. Abstract terms are so called as being arrived at
by a process of Abstraction. What is meant by Abstrac
tion will be clear from a single instance. The mind, in
contemplating a number of substances, may draw off, or
abstract, its attention from all their other characteristics,
and fix it only on some point, or points, which they have
in common. Thus, in contemplating a number of three-
cornered objects, we may draw away our attention from
all their other qualities, and fix it exclusively upon their
three-corneredness, thus constituting the abstract notion
of ' triangle/ Abstraction may be performed equally
well in the case of a single object : but the mind would
not originally have known on what points to fix its
attention except by a comparison of individuals.
1 Since things cannot be spoken of except by their names, there is
a constantly recurring source of confusion between the thing itself
and the name of it. Take for instance ' whiteness.' The attribute
whiteness is a thing, the word ' whiteness ' is a term.
OF THE DIVISION OF TERMS. 1J
§98. Abstraction too may be performed upon attri
butes as well as substances. Thus, having by abstraction
already arrived at the notion of triangle, square, and so on,
we may fix our attention upon what these have in common,
and so rise to the higher abstraction of ' figure/ As
thought becomes more complex, we may have abstraction
on abstraction and attributes of attributes. But, however
many steps may intervene, attributes may always be traced
back to substances at last. For attributes of attributes
can mean at bottom nothing but the co-existence of attri
butes in, or in connection with, the same substances.
§ 99. We have said that abstract terms are so called, as
being arrived at by abstraction : but it must not be inferred
from this statement that all terms which are arrived at by
abstraction are abstract. If this were so, all names would
be abstract except proper names of individual substances.
All common terms, including attributives, are arrived at
by abstraction, but they are not therefore abstract terms.
Those terms only are called abstract, which cannot be
applied to substances at all. The terms ' man ' and
'human' are names of the same substance of which
Socrates is a name. Humanity is a name only of certain
attributes of that substance, namely those which are shared
by others. All names of concrete things then are concrete,
whether they denote them individually or according to
classes, and whether directly and in themselves, or in
directly, as possessing some given attribute.
§ 100. By a 'concrete thing" is meant an individual
substance conceived of with all its attributes about it.
2 8 OF THE DIVISION OF TERMS.
The term is not confined to material substances. A
spirit conceived of under personal attributes is as concrete
as plum-pudding.
§ 101. Since things are divided exhaustively into sub
stances and attributes, it follows that any term which is
not the name of a thing capable of being conceived to
exist by itself, must be an abstract term. Individual
substances can alone be conceived to exist by themselves :
all their qualities, actions, passions, and inter-relations, all
their states, and all events with regard to them, presuppose
the existence of these individual substances. All names
therefore of such things as those just enumerated are
abstract terms. The term 'action,' for instance, is an
abstract term. For how could there be action without an
agent ? The term ' act ' also is equally abstract for the
same reason. The difference between 'action' and 'act'
is not the difference between abstract and concrete, but
the difference between the name of a process and the
name of the corresponding product. Unless acts can be
conceived to exist without agents they are as abstract as
the action from which they result.
§ 102. Since every term must be either abstract or
concrete, it may be asked — Are attributives abstract or
concrete ? The answer of course depends upon whether
they are names of substances or names of attributes. But
attributives, it must be remembered, are never directly
names of anything, in the way that subject-terms are ;
they are only names of things in virtue of being predicated
of them. Whether an attributive is abstract or concrete,
OF THE DIVISION OF TERMS. 29
depends on the nature of the subject of which it is asserted
or denied. When we say ' This man is noble/ the term
' noble ' is concrete, as being the name of a substance :
but when we say ' This act is noble,' the term ' noble ' is
abstract, as being the name of an attribute.
§ 103. The division of terms into Abstract and Concrete
is based upon the kind of thing signified It involves no
reference to actual existence. There are imaginary as
well as real substances. Logically a centaur is as much
a substance as a horse.
Singular and Common Terms.
§ 104. A Singular Term is a name which can be
applied, in the same sense, to one thing only, e. g. ' John/
' Paris/ ' the capital of France/ ' this pen.'
§ 105. A Common Term is a name which can be
applied, in the same sense, to a class of things, e. g. ' man/
'metropolis/ 'pen/
In order that a term may be applied in the same sense
to a number of things, it is evident that it must indicate
attributes which are common to all of them. The term
' John ' is applicable to a number of things, but not in the
same sense, as it does not indicate attributes.
§ 106. Common terms are formed, as we have seen
already (§ 99), by abstraction, i. e. by withdrawing the
attention from the attributes in which individuals differ,
and concentrating it upon those which they have in
common.
30 OF THE DIVISION OF TERMS.
§ 107. A class need not necessarily consist of more than
two things. If the sun and moon were the only
heavenly bodies in the universe, the word ' heavenly body '
would still be a common term, as indicating the attributes
which are possessed alike by each.
§ 108. This being so, it follows that the division of
terms into singular and common is as exhaustive as the
preceding ones, since a singular term is the name of one
thing and a common term of more than one. It is in
different whether the thing in question be a substance or
an attribute ; nor does it matter how complex it may be,
so long as it is regarded by the mind as one.
§ 109. Since every term must thus be either singular or
common, the members of the preceding divisions must
find their place under one or both heads of this one.
Subject-terms may plainly fall under either head of singular
or common: but attributives are essentially common terms.
Such names as ' green,' ' gentle/ ' incongruous ' are appli
cable, strictly in the same sense, to all the things which
possess the attributes which they imply.
§ 110. Are abstract terms then, it may be asked,
singular or common ? To this question we reply — That
depends upon how they are used. The term ' virtue/ for
instance, in one sense, namely, as signifying moral excel
lence in general, without distinction of kind, is strictly a
singular term, as being the name of one attribute : but as
applied to different varieties of moral excellence — justice,
generosity, gentleness and so on — it is a common
term, as being a name which is applicable, in the same
OF THE DIVISION OF TERMS. 31
sense, to a class of attributes. Similarly the term ' colour/
in a certain sense, signifies one unvarying attribute
possessed by bodies, namely, the power of affecting the
eye, and in this sense it is a singular term : but as applied
to the various ways in which the eye may be affected, it is
evidently a common term, being equally applicable to red,
blue, green, and every other colour. As soon as we begin
to abstract from attributes, the higher notion becomes a
common term in reference to the lower. By a 'higher
notion' is meant one which is formed by a further process
of abstraction. The terms ' red/ ' blue/ ' green/ etc., are
arrived at by abstraction from physical objects ; ' colour '
is arrived at by abstraction from them, and contains
nothing, but what is common to all. It therefore applies
in the same sense to each, and is a common term in
relation to them.
§ 111. A practical test as to whether an abstract term,
in any given case, is being used as a singular or common
term, is to try whether the indefinite article or the sign of
the plural can be attached to it. The term ' number/ as
the name of a single attribute of things, admits of neither
of these adjuncts : but to talk of ' a number ' or ' the
numbers, two, three, four/ etc., at once marks it as a
common term. Similarly the term 'unity' denotes a
single attribute, admitting of no shades of distinction : but
when a writer begins to speak of ' the unities ' he is evi
dently using the word for a class of things of some kind or
other, namely, certain dramatical proprieties of composi
tion.
3 2 OF THE DIVISION OF TERMS.
Proper Names and Designations.
§ 112. Singular terms may be subdivided into Proper
Names and Designations.
§ 113. A Proper Name is a permanent singular term
applicable to a thing in itself; a Designation is a singular
term devised for the occasion, or applicable to a thing only
in so far as it possesses some attribute.
§ 114. 'Homer' is a proper name; 'this man/ 'the
author of the Iliad ' are designations.
§ 115. The number of things, it is clear, is infinite.
For, granting that the physical universe consists of a
definite number of atoms — neither one more nor one
less — still we are far from having exhausted the possible
number of things. All the manifold material objects, which
are made up by the various combinations of these atoms,
constitute separate objects of thought, or things, and the
mind has further an indefinite power of conjoining and
dividing these objects, so as to furnish itself with materials
of thought, and also of fixing its attention by abstraction
upon attributes, so as to regard them as things, apart from
the substances to which they belong.
§ 116. This being so, it is only a very small number
of things, which are constantly obtruding themselves upon
the mind, that have singular terms permanently set apart
to denote them. Human beings, some domestic animals,
and divisions of time and place, have proper names
assigned to them in most languages, e. g. ' John/ ' Mary/
8 Grip/ ' January/ < Easter/ ' Belgium/ ' Brussels/ ' the
OF THE DIVISION OF TERMS. 33
Thames/ 'Ben-Nevis/ Besides these, all abstract terms,
when used without reference to lower notions, are of the
nature of proper names, being permanently set apart
to denote certain special attributes, e. g. ' benevolence/
'veracity/ 'imagination/ ' indigestibility/ 'retrenchment.'
§ 117. But the needs of language often require a
singular term to denote some thing which has not had
a proper name assigned to it. This is effected by taking
a common term, and so limiting it as to make it appli
cable, under the given circumstances, to one thing only.
Such a limitation may be effected in English by prefixing
a demonstrative or the definite article, or by appending a
description, e. g. ' this pen/ ' the sofa/ ' the last rose of
summer.' When a proper name is unknown, or for some
reason, unavailable, recourse may be had to a designation,
e. g. ' the honourable member who spoke last but one/
Collective Terms.
§ 118. The division of terms into singular and common
being, like those which have preceded it, fundamental and
exhaustive, there is evidently no room in it for a third
class of Collective Terms. Nor is there any distinct class
of terms to which that name can be given. The same
term may be used collectively or distributively in different
relations. Thus the term ' library/ when used of the
books which compose a library, is collective ; when used
of various collections of books, as the Bodleian, Queen's
library, and so on, it is distributive, which, in this case, is
the same thing as being a common term.
D
34 OF THE DIVISION OF TERMS.
§ 119. The distinction between the collective and dis
tributive use of a term is of importance, because the
confusion of the two is a favourite source of fallacy.
When it is said ' The plays of Shakspeare cannot be read
in a day/ the proposition meets with a very different
measure of acceptance according as its subject is under
stood collectively or distributively. The word ' all ' is
perfectly ambiguous in this respect. It may mean all
together or each separately — two senses which are distin
guished in Latin by ' totus ' or ' cunctus,' for the collective,
and ' omnis ' for the distributive use.
§ 120. What is usually meant however when people
speak of a collective term is a particular kind of singular
term.
§ 121. From this point of view singular terms may be
subdivided into Individual and Collective, by an Individual
Term being meant the name of one object, by a Collective
Term the name of several considered as one. ' This key '
is an individual term ; * my bunch of keys ' is a collective
term.
§ 122. A collective term is quite as much the name of
one thing as an individual term is, though the thing in
question happens to be a group. A group is one thing, if
we choose to think of it as one. For the mind, as we have
already seen, has an unlimited power of forming its own
things, or objects of thought. Thus a particular peak in
a mountain chain is as much one thing as the chain itself,
though, physically speaking, it is inseparable from it, just
as the chain itself is inseparable from the earth's surface.
OF THE DIVISION OF TERMS. 35
In the same way a necklace is as much one thing as the
individual beads which compose it.
§ 123. We have just seen that a collective term is the
name of a group regarded as one thing : but every term
which is the name of such a group is not necessarily a
collective term. ' London/ for instance, is the name of a
group of objects considered as one thing. But ' London '
is not a collective term, whereas ' flock/ ' regiment/ and
' senate ' are. Wherein then lies the difference ? It lies
in this — that flock, regiment and senate are groups
composed of objects which are, to a certain extent, similar,
whereas London is a group made up of the most dis
similar objects — streets and squares and squalid slums,
fine carriages and dirty faces, and so on. In the case of
a true collective term all the members of the group will
come under some one common name. Thus all the
members of the group, flock of sheep, come under the
common name 'sheep/ all the members of the group
' regiment ' under the common name, ' soldier/ and so
on.
§ 124. The subdivision of singular terms into individual
and collective need not be confined to the names of
concrete things. An abstract term like ' scarlet/ which
is the name of one definite attribute, may be reckoned
' individual/ while a term like ' human nature/ which is
the name of a whole group of attributes, would more fitly
be regarded as collective.
§ 125. The main division of terms, which we have
been discussing, into singular and collective, is based
D 2
36 OF THE DIVISION OF TERMS.
upon their Quantity in Extension. This phrase will be
explained presently.
§ 126. We come now to a threefold division of terms
into Positive, Privative and Negative. It is based upon an
implied two-fold division into positive and non-positive,
the latter member being subdivided into Privative and
Negative.
Term
Positive
1
Non-Positive
Privative
1
Negative
If this division be extended, as it sometimes is, to
terms in general, a positive term must be taken to mean
only the definite, -or comparatively definite, member of an
exhaustive division in accordance with the law of excluded
middle (§ 25). Thus 'Socrates' and 'man' are positive,
as opposed to ' not-Socrates ' and ' not-man.'
§ 127. The chief value of the division, however, and
especially of the distinction drawn between privative and
negative terms, is in relation to attributives.
From this point of view we may define the three classes
of terms as follows :
A Positive Term signifies the presence of an attribute,
e. g. •' wise/ ' full.'
A Negative Term signifies merely the absence of an
attribute, e, g. c not-wise,' ' not-full.'
A Privative Term signifies the absence of an attribute
OF THE DIVISION OF TERMS. 37
in a subject capable of possessing it, e. g. ' unwise/
' empty ' *.
§ 128. Thus a privative term stands midway in meaning
between the other two, being partly positive and partly
negative — negative in so far as it indicates the absence of
a certain attribute, positive in so far as it implies that the
thing which is declared to lack that attribute is of such a
nature as to be capable of possessing it. A purely
negative term conveys to the mind no positive information
at all about the nature of the thing of which it is pre
dicated, but leaves us to seek for it among the universe of
things which fail to exhibit a given attribute.
A privative term, on the other hand, restricts us within
a definite sphere. The term ' empty ' restricts us within
the sphere of things which are capable of fulness, that is,
if the term be taken in its literal sense, things which
possess extension in three dimensions.
§ 129. A positive and a negative term, which have the
same matter, must exhaust the universe between them,
e.g. 'white' and 'not-white/ since, according to the law
of excluded middle, everything must be either one or the
other. To say, however, that a thing is ' not- white ' is
merely to say that the term ' white ' is inapplicable to it.
'Not-white' may be predicated of things which do not
1 A privative term is usually defined to mean one which signifies
the absence of an attribute where it was once possessed, or might
have been expected to be present, e. g. ' blind.' The utility of the
slight extension of meaning here assigned to the expression will, it
is hoped, prove its justification.
38 OF THE DIVISION OF TERMS.
possess extension as well as of those which do. Such a
pair of terms as 'white' and 'not-white,' in their relation
to one another, are called Contradictories.
§ 130. Contrary terms must be distinguished from
contradictory. Contrary terms are those which are most
opposed under the same head. Thus 'white' and 'black'
are contrary terms, being the most opposed under the
same head of colour. ' Virtuous ' and ' vicious ' again are
contraries, being the most opposed under the same head
of moral quality.
§131. A positive and a privative term in the same
matter will always be contraries, e. g. ' wise ' and ' unwise/
' safe ' and l unsafe ' : but contraries do not always assume
the shape of positive and privative terms, but may both be
positive in form, e. g. ' wise ' and ' foolish,' ' safe ' and
' dangerous/
§ 132. Words which are positive in form are often
privative in meaning, and vice versa. This is the case,
for instance, with the word ' safe/ which connotes nothing
more than the absence of danger. We talk of a thing
involving ' positive danger ' and of its being ' positively
unsafe' to do so and so. 'Unhappy/ on the other hand,
signifies the presence of actual misery. Similarly in Latin
'inutilis' signifies not merely that there is no benefit to be
derived from a thing, but that it is positively injurious. All
such questions, however, are for the grammarian or
lexicographer, and not for the logician. For the latter it
is sufficient to know that corresponding to every term
which signifies the presence of some attribute there may
OF THE DIVISION OF TERMS. 39
be imagined another which indicates the absence of the
same attribute, where it might be possessed, and a third
which indicates its absence, whether it might be possessed
or not.
§ 133. Negative terms proper are formed by the prefix
' not-' or ' non-,' and are mere figments of logic. We do
not in practice require to speak of the whole universe of
objects minus those which possess a given attribute or
collection of attributes. We have often occasion to speak
of things which might be wise and are not, but seldom, if
ever, of all things other than wise.
§ 134. Every privative attributive has, or may have, a
corresponding abstract term, and the same is the case
with negatives : for the absence of an attribute, is itself an
attribute. Corresponding to 'empty/ there is 'emptiness';
corresponding to ' not-full ' there may be imagined the
term ' not-fulness.'
§ 135. The contrary of a given term always involves
the contradictory, but it involves positive elements as well.
Thus ' black ' is ' not-white,' but it is something more
besides. Terms which, without being directly contrary,
involve a latent contradiction, are called Repugnant, e. g.
' red ' and ' blue.' All terms whatever which signify
attributes that exclude one another may be called In
compatible.
§ 136. The preceding division is based on what is
known as the Quality of terms, a positive term being said
to differ in quality from a non-positive one.
40 OF THE DIVISION OF TERMS.
Univocal and Equivocal Terms.
§ 137. A term is said to be Univocal, when it has one
and the same meaning wherever it occurs. A term which
has more than one meaning is called Equivocal. ' Jam
pot/ ' hydrogen ' are examples of univocal terms ; * pipe '
and ' suit ' of equivocal.
§ 138. This division does not properly come within the
scope of logic, since it is a question of language, not of
thought. From the logician's point of view an equivocal
term is two or more different terms, for the definition in
each sense would be different.
§ 139. Sometimes a third member is added to the same
division under the head of Analogous Terms. The word
' sweet/ for instance, is applied by analogy to things so
different in their own nature as a lump of sugar, a young
lady, a tune, a poem, and so on. Again, because the
head is the highest part of man, the highest part of
a stream is called by analogy 'the head.' It is plainly
inappropriate to make a separate class of analogous terms.
Rather, terms become equivocal by being extended by
analogy from one thing to another.
Absolute and Relative Terms.
§ 140. An Absolute term is a name given to a thing
without reference to anything else.
§ 141. A Relative term is a name given to a thing with
direct reference to some other thing.
§ 142. ' Hodge ' and ' man ' are absolute terms. ' Hus
band/ ' father/ ' shepherd ' are relative terms. ' Husband '
OF THE DIVISION OF TERMS. 41
conveys a direct reference to * wife/ ' father ' to ' child/
' shepherd ' to ' sheep/ Given one term of a relation, the
other is called the correlative, e. g. * subject ' is the ' corre
lative of ' ruler/ and conversely ' ruler ' of ' subject/ The
two terms are also spoken of as a pair of correlatives.
§ 143. The distinction between relative and absolute
applies to attributives as well as subject-terms. ' Greater/
' near/ * like/ are instances of attributives which everyone
would recognise as relative.
§ 144. A relation, it will be remembered, is a kind of
attribute, differing from a quality in that it necessarily
involves more substances than one. Every relation is at
bottom a fact, or series of facts, in which two or more
substances play a part. A relative term connotes this fact
or facts from the point of view of one of the substances, its
correlative from that of the other. Thus 'ruler' and
' subject ' imply the same set of facts, looked at from
opposite points of view. The series of facts itself, regarded
from either side, is denoted by the corresponding abstract
terms, ' rule ' and ' subjection/
§ 145. It is a nice question whether the abstract names
of relations should themselves be considered relative terms.
Difficulties will perhaps be avoided by confining the
expression 'relative term' to names of concrete things.
' Absolute/ it must be remembered, is a mere negative of
' relative/ and covers everything to which the definition of
the latter does not strictly apply. Now it can hardly be
said that ' rule ' is a name given to a certain abstract thing
with direct reference to some other thing, namely, subjec-
42 OF THE DIVISION OF TERMS.
tion. Rather ' rule ' and ' subjection ' are two names for
identically the same series of facts, according to the side
from which we look at them. ' Ruler ' and ' subject,' on
the other hand, are names of two distinct substances, but
each involving a reference to the other.
§ 146. This division then may be said to be based on
the number of things involved in the name.
Connotative and Non-Connotative Terms,
§ 147. Before explaining this division, it is necessary to
treat of what is called the Quantity of Terms.
Quantity of Terms.
§ 148. A term is possessed of quantity in two ways —
(1) In Extension;
(2) In Intension.
§ 149. The Extension of a term is the number of things
to which it applies.
§ 150. The Intension of a term is the number of attri
butes which it implies.
§ 151. It will simplify matters to bear in mind that the
intension of a term is the same thing as its meaning. To
take an example, the term ' man ' applies to certain
things, namely, all the members of the human race that
have been, are, or ever will be : this is its quantity in exten
sion. But the term ' man ' has also a certain meaning,
and implies certain attributes — rationality, animality, and
a definite bodily shape : the sum of these attributes consti
tutes its quantity in intension.
OF THE DIVISION OF TERMS. 43
§ 152. The distinction between the two kinds of quantity
possessed by a term is also conveyed by a variety of
expressions which are here appended.
Extension = breadth = compass = application = deno
tation.
Intension = depth = comprehension = implication = con
notation.
Of these various expressions, ' application ' and ' impli
cation ' have the advantage of most clearly conveying their
own meaning. ' Extension ' and ' intension/ however, are
more usual ; and neither ' implication ' nor ' connotation '
is quite exact as a synonym for ' intension.' (§ 164.)
§ 153. We now return to the division of terms into con-
notative and non-connotative.
§ 154. A term is said to connote attributes, when it im
plies certain attributes at the same time that it applies to
certain things distinct therefrom 1.
§ 155. A term which possesses both extension and
intension, distinct from one another, is connotative.
§ 156. A term which possesses no intension (if that
be possible) or in which extension and intension coincide
is non-connotative.
§ 157. The subject-term, 'man,' and its corresponding
attributive, ' human/ have both extension and intension,
distinct from one another. They are therefore connota-
1 Originally ' connotative ' was used in the same sense in which
we have used ' attributive,' for a word which directly signifies the
presence of an attribute and indirectly applies to a subject. In this,
its original sense, it was the subject which was said to be connoted,
and not the attribute.
44 OF THE DIVISION OF TERMS.
tive. But the abstract term, ' humanity/ denotes the very
collection of attributes, which was before connoted by the
concrete terms, ' man ' and ' human/ In this case, there
fore, extension and intension coincide, and the term is
non-connotative.
§ 158. The above remark must be understood to be
limited to abstract terms in their singular sense. When
employed as common terms, abstract terms possess both
extension and intension distinct from one another. Thus
the term ' colour ' applies to red, blue, and yellow, and at
the same time implies (i.e. connotes), the power of affect
ing the eye.
§ 159. Since all terms are names of things, whether
substances or attributes, it is clear that all terms must
possess extension, though the extension of singular terms
is the narrowest possible, as being confined to one thing.
§ 160. Are there then any terms which possess no
intension ? To ask this, is to ask — Are there any terms
which have absolutely no meaning ? It is often said that
proper names are devoid of meaning, and the remark is,
in a certain sense, true. When we call a being by the
name ' man,' we do so because that being possesses
human attributes, but when we call the same being by the
name, ' John/ we do not mean to indicate the presence of
any Johannine attributes. We simply wish to distinguish
that being, in thought and language, from other beings of
the same kind. Roughly speaking, therefore, proper
names are devoid of meaning or intension. But no name
can be entirely devoid of meaning. For, even setting
OF THE DIVISION OF TERMS. 45
aside the fact, which is not universally true, that proper
names indicate the sex of the owner, the mere act of
giving a name to a thing implies at least that the thing
exists, whether in fact or thought ; it implies what we may
call 'thinghood': so that every term must carry with it
some small amount of intension.
§ 161. From another point of view, however, proper
names possess more intension than any other terms. For
when we know a person, his name calls up to our minds
all the individual attributes with which we are familiar, and
these must be far more numerous than the attributes which
are conveyed by any common term which can be applied
to him. Thus the name ' John ' means more to a person
who knows him than ' attorney/ ' conservative/ ' scamp/
or ' vestry-man/ or any other term which may happen to
apply to him. This, however, is the acquired intension of
a term, and must be distinguished from the original inten
sion. The name ' John ' was never meant to indicate the
attributes which its owner has, as a matter of fact, de
veloped. He would be John all the same, if he were none
of these.
§ 162. Hitherto we have been speaking only of christen
ing-names, but it is evident that family names have a cer
tain amount of connotation from the first. For when we
dub John with the additional appellation of Smith, we do
not give this second name as a mere individual mark, but
intend thereby to indicate a relationship to other persons.
The amount of connotation that can be conveyed by
proper names is very noticeable in the Latin language.
46 OF THE DIVISION OF TERMS.
Let us take for an example the full name of a distinguished
Roman — Publius Cornelius Scipio JSmilianus Africanus
minor. Here it is only the praenomen, Publius, that can
be -said to be a mere individual mark, and even this
distinctly indicates the sex of the owner. The nomen
proper, Cornelius, declares the wearer of it to belong to
the illustrious gens Cornelia. The cognomen, Scipio,
further specifies him as a member of a distinguished
family in that gens. The agnomen adoptivum indicates
his transference by adoption from one gens to another.
The second agnomen recalls the fact of his victory over
the Carthaginians, while the addition of the word ' minor '
distinguishes him from the former wearer of the same
title. The name, instead of being devoid of meaning, is
a chapter of history in itself. Homeric epithets, such as
' The Cloud-compeller/ ' The Earth-shaker ' are instances
of intensive proper names. Many of our own family
names are obviously connotative in their origin, implying
either some personal peculiarity, e.g. Armstrong, Cruik-
shank, Courteney ; or the employment, trade or calling of
the original bearer of the name, Smith, Carpenter, Baker,
Clark, Leach, Archer, and so on; or else his abode,
domain or nationality, as De Caen, De Montmorency,
French, Langley; or simply the fact of descent from
some presumably more noteworthy parent, as Jackson,
Thomson, Fitzgerald, O'Connor, Macdonald, Apjohn,
Price, Davids, etc. The question, however, whether
a term is connotative or not, has to be decided, not by
its origin, but by its use. We have seen that there are
OF THE DIVISION OF TERMS. 47
some proper names which, in a rough sense, may be said
to possess no intension.
§ 163. The other kind of singular terms, namely, de
signations (§ 113) are obviously connotative. We cannot
employ even the simplest of them without conveying more
or less information about the qualities of the thing which
they are used to denote. When, for instance, we say
' this table,' ' this book/ we indicate the proximity to the
speaker of the object in question. Other designations
have a higher degree of intension, as when we say ' the
present prime minister of England/ 'the honourable
member who brought forward this motion to-night.'
Such terms have a good deal of significance in them
selves, apart from any knowledge we may happen to
possess of the individuals they denote.
§ 164. We have seen that, speaking quite strictly, there
are no terms which are non-connotative : but, for practical
purposes, we may apply the expression to proper names,
on the ground that they possess no intension, and to
singular abstract terms on the ground that their extension
and intension coincide. In the latter case it is indifferent
whether we call the quantity extension or intension. Only
we cannot call it ' connotation/ because that implies two
quantities distinct from one another. A term must already
denote a subject before it can be said to connote its
attributes.
§ 165. The division of terms into connotative and non-
connotative is based on their possession of one quantity
or two.
CHAPTER IV.
Of the Law of Inverse Variation of
Extension and Intension.
§ 166. IN a series of terms which fall under one an
other, as the extension decreases, the intension increases,
and vice versa. Take for instance the following series —
Thing
Substance
I
Matter
Organism
Animal
I
Vertebrate
Mammal
Ruminant
Sheep
This sheep.
Here the term at the top possesses the widest possible
extension, since it applies to everything. But at the same
time it possesses the least possible amount of intension,
implying nothing more than mere existence, whether in
fact or thought. On the other hand, the term at the
bottom possesses the greatest amount of intension, since
OF THE LAW OF INVERSE VARIATION, ETC. 49
it implies all the attributes of an individual superadded to
those of the class to which it belongs : but its extension is
the narrowest possible, being limited to one thing.
§ 167. At each step in the descent from the term at the
top, which is called the ' Summum genus,' to the indi
vidual, we decrease the extension by increasing the inten
sion. Thus by adding on to the bare notion of a thing
the idea of independent existence, we descend to the term
' substance.' This process is known as Determination, or
Specialisation.
§ 168. Again, by withdrawing our attention from the
individual characteristics of a particular sheep, and fixing
it upon those which are common to it with other animals
of the same kind, we arrive at the common term, 'sheep.'
Here we have increased the extension by decreasing the
intension. This process is known as Generalisation.
§ 169. Generalisation implies abstraction, but we may
have abstraction without generalisation.
§ 170. The following example is useful, as illustrating
to the eye how a decrease of extension is accompanied by
an increase of intension. At each step of the descent
here we visibly tack on a fresh attribute '.
Ship
I
Steam-ship
Screw steam-ship
Iron screw steam-ship
I
British iron screw steam-ship.
1 This example is borrowed from Professor Jevons.
E
50 OF THE LA W OF INVERSE VARIA TIONy ETC.
Could we see the classes denoted by the names the
pyramid would be exactly inverted.
§ 171. The law of inverse variation of extension and
intension must of course be confined to the inter-relations
of a series of terms of which each can be predicated of the
other until we arrive at the bottom of the scale. It is not
meant to apply to the extension and intension of the same
term. The increase of population does not add to the
meaning of ' baby/
PART II.— OF PROPOSITIONS.
CHAPTER I.
Of the Proposition as distinguished from
other Sentences.
§ 172. As in considering the term, we found occasion
to distinguish it from words generally, so now, in con
sidering the proposition, it will be well to begin by distin
guishing it from other sentences.
§ 173. Every proposition is a sentence, but every sen
tence is not a proposition.
§ 174. The field of logic is far from being conterminous
with that of language. Language is the mirror of man's
whole nature, whereas logic deals with language only so
far as it gives clothing to the products of thought in the
narrow sense which we have assigned to that term.
Language has materials of every sort lying strewn about,
among which the logician has to seek for his proper
implements.
§ 175. Sentences may be employed for a variety of
purposes —
(i) To ask a question;
E 2
52 OF THE PROPOSITION AS DISTINGUISHED
(2) To give an order;
(3) To express a feeling ;
(4) To make a statement.
These various uses give rise respectively to
(1) The Interrogative ;
(2) The Imperative ;
(3) The Exclamatory ;
f Indicative
(4) The Lnunciative < _
( Potential
>• Sentence.
It is with the last of these only that logic is concerned.
§ 176. The proposition, therefore, corresponds to the
Indicative and Potential, or Conditional, sentences of
grammar. For it must be borne in mind that logic
recognises no difference between a statement of fact and
a supposition. ' It may rain to-morrow ' is as much a
proposition as * It is raining now.'
§ 177. Leaving the grammatical aspect of the proposi
tion, we must now consider it from the purely logical
point of view.
§ 178. A proposition is a judgement expressed in
words ; and a judgement is a direct comparison between
two concepts.
§ 179. The same thing may be expressed more briefly
by saying that a proposition is a direct comparison be
tween two terms.
§ 180. We say 'direct comparison/ because the syllo
gism also may be described as a comparison between two
terms : but in the syllogism the two terms are compared
indirectly, or by means of a third term.
FROM OTHER SENTENCES. 53
§ 181. A proposition may be analysed into two terms
and a Copula, which is nothing more than the sign of
agreement or disagreement between them.
§ 182. The two terms are called the Subject and the
Predicate (§ 58).
§ 183. The Subject is that of which something is
stated.
§ 184. The Predicate is that which is stated of the
subject.
§ 185. Hence the subject is thought of for its own
sake, and the predicate for the sake of the subject.
CHAPTER II.
Of the Copula.
§ 186. THERE are two kinds of copula, one for affirma
tive and one for negative statements.
§ 187. Materially the copula is expressed by some part
of the verb ' to be/ with or without the negative, or else
is wrapped up in some inflexional form of a verb.
§ 188. The material form of the copula is an accident
of language, and a matter of indifference to logic. ' The
kettle boils ' is as logical a form of expression as ' The
kettle is boiling/ For it must be remembered that the
word ' is ' here is a mere sign of agreement between the
two terms, and conveys no notion of actual existence.
We may use it indeed with equal propriety to express
non-existence, as when we say ' An idol is nothing.'
§ 189. When the verb 'to be' expresses existence in
fact it is known in grammar as ' the substantive verb/ In
this use it is predicate as well as copula, as when we say
' God is/ which may be analysed, if we please, into ' God
is existent/
§ 190. We have laid down above that there are two
kinds of copula, affirmative and negative : but some
logicians have maintained that the copula is always affir
mative.
OF THE COPULA. 55
§ 191. What then, it may be asked, on this view, is the
meaning of negative propositions ? To which the answer
is, that a negative proposition asserts an agreement be
tween the subject and a negative term. When, for
instance, we say ' The whale is not a fish,' this would be
interpreted to mean * The whale is a not-fish/
§ 192. Undoubtedly any negative proposition may be
exhibited in an affirmative form, since, by the law of
excluded middle, given a pair of contradictory terms,
wherever the one can be asserted, the other can be
denied, and vice versa. We shall find later on that this
principle gives rise to one of the forms of immediate
inference. The only question then can be, which is the
more natural and legitimate form of expression. It seems
simpler to suppose that we assert the agreement of 'whale'
with 'not-fish' by implication only, and that what we
directly do is to predicate a disagreement between 'whale'
and the positive attributes connoted by ' fish.' For since
' not-fish ' must apply to every conceivable object of
thought except those which fall under the positive term
' fish,' to say that a whale is a ' not-fish,' is to say that
we have still to search for ' whale ' throughout the whole
universe of being, minus a limited portion ; which is only
a more clumsy way of saying that it is not to be found in
that portion.
§ 193. Again, the term ' not-fish ' must be understood
either in its intension or in its extension. If it be under
stood in its intension, what it connotes is simply the
absence of the positive qualities which constitute a fish,
56 OF THE COPULA.
a meaning which is equally conveyed by the negative
form of proposition. We gain nothing in simplicity by
thus confounding assertion with denial. If, on the other
hand, it is to be taken in extension, this involves the
awkwardness of supposing that the predicative power of a
term resides in its extensive capacity.
§ 194. We therefore recognise predication as being of
two kinds — affirmation and negation — corresponding to
which there are two forms of copula.
§ 195. On the other hand, other logicians have main
tained that there are many kinds of copula, since the
copula must vary according to the various degrees of
probability with which we can assert or deny a predicate
of a subject. This view is technically known as the
doctrine of
The Modality of the Copula.
§ 196. It may plausibly be maintained that the division
of propositions into affirmative and negative is not an
exhaustive one, since the result of an act of judgement is
not always to lead the rnind to a clear assertion or a clear
denial, but to leave it in more or less doubt as to whether
the predicate applies to the subject or not. Instead of
saying simply A is B, or A is not B, we may be led to
one of the following forms of proposition —
A is possibly B.
A is probably B.
A is certainly B.
OF THE COPULA. 57
The adverbial expression which thus appears to qualify
the copula is known as ' the mode.'
§ 197. When we say ' The accused may be guilty' we
have a proposition of very different force from ' The
accused is guilty/ and yet the terms appear to be the
same. Wherein then does the difference lie ? ' In the
copula ' would seem to be the obvious reply. We seem
therefore driven to admit that there are as many different
kinds of copula as there are different degrees of assurance
with which a statement may be made.
§ 198. But there is another way in which modal pro
positions may be regarded. Instead of the mode being
attached to the copula, it may be considered as itself
constituting the predicate, so that the above propositions
would be analysed thus —
That A is B, is possible.
That A is B, is probable.
That A is B, is certain.
§ 199. The subject here is itself a proposition of which
we predicate various degrees of probability. In this way
the division of propositions into affirmative and negative
is rendered exhaustive. For wherever before we had a
doubtful assertion, we have now an assertion of doubt
fulness.
§ 200. If degrees of probability can thus be eliminated
from the copula, much more so can expressions of time,
which may always be regarded as forming part of the pre
dicate. ' The sun will rise to-morrow ' may be analysed
into ' The sun is going to rise to-morrow.' In either
58 OF THE COPULA.
case the tense belongs equally to the predicate. It is
often an awkward task so to analyse propositions relative
to past or future time as to bring out the copula under
the form ' is ' or 'is not ' : but fortunately there is no
necessity for so doing, since, as has been said before
(§ 188), the material form of the copula is a matter of
indifference to logic. Indeed in affirmative propositions
the mere juxtaposition of the subject and predicate is
often sufficient to indicate their agreement, e. g. ' Most
haste, worst speed,' xa^€7r" r" xa\d. It is because all
propositions are not affirmative that we require a copula
at all. Moreover the awkwardness of expression just
alluded to is a mere accident of language. In Latin
we may say with equal propriety ' Sol orietur eras ' or
' Sol est oriturus eras ' ; while past time may also be
expressed in the analytic form in the case of deponent
verbs, as ' Caesar est in Galliam profectus ' — ' Caesar is
gone into Gaul.'
§ 201. The copula then may always be regarded as
pure, that is, as indicating mere agreement or disagree
ment between the two terms of the proposition.
CHAPTER III.
Of the Divisions of Propositions.
§ 202. THE most obvious and the most important
division of propositions is into true and false, but with
this we are not concerned. Formal logic can recognise
no difference between true and false propositions. The
one is represented by the same symbols as the other.
§ 203. We may notice, however, in passing, that truth
and falsehood are attributes of propositions and of pro
positions only. For something must be predicated, i. e.
asserted or denied, before we can have either truth or
falsehood. Neither concepts or terms, on the one hand,
nor reasonings, on the other, can properly be said to be
true or false. In the mere notion of a Centaur or of a
black swan there .is neither truth nor falsehood; it is not
until we make some statement about these things, such as
that 'black swans are found in Australia,' or 'I met a
Centaur in the High Street yesterday/ that the question of
truth or falsehood comes in. In such expressions as a
1 true friend ' or ' a false patriot ' there is a tacit reference
to propositions. We mean persons of whom the terms
' friend ' and ' patriot ' are truly or falsely predicated.
Neither can we with any propriety talk of true or false
60 OF THE DIVISIONS OF PROPOSITIONS.
reasoning. Reasoning is either valid or invalid : it is
only the premisses of our reasonings, which are proposi
tions, that can be true or false. We may have a perfectly
valid process of reasoning which starts from a false
assumption and lands us in a false conclusion.
§ 204. All truth and falsehood then are contained in
propositions ; and propositions are divided according to the
Quality of the Matter into true and false. But the consider
ation of the matter is outside the sphere of formal or de
ductive Logic. It is the problem of inductive logic to
establish, if possible, a criterion of evidence whereby the
truth or falsehood of propositions may be judged (§ 2).
§ 205. Another usual division of propositions is into
Pure and Modal, the latter being those in which the
copula is modified by some degree of probability. This
division is excluded by the view which has just been
taken of the copula, as being always simply affirmative or
simply negative.
§ 206. We are left then with the following divisions of
propositions —
Proposition •<
Simple
)
Complex
I Conjunctive
( Disjunctive
V according to Form.
Verbal
) according to
Real
^ Matter.
Universal
( Singular
( General
(according to
Particular
\ Indefinite
( (strictly) Particular
j Quantity.
Affirmative
! according to
Negative
Quality.
OF THE DIVISIONS OF PROPOSITIONS. 6 1
Simple and Complex Propositions.
§ 207. A Simple Proposition is one in which a pre
dicate is directly affirmed or denied of a subject, e. g. ' Rain
is falling.'
§ 208. A simple proposition is otherwise known as
Categorical.
§ 209. A Complex Proposition is one in which a state
ment is made subject to some condition, e. g. ' If the wind
drops, rain will fall.'
§ 210. Hence the complex proposition is also known
as Conditional.
§ 211. Every complex proposition consists of two
parts —
(1) Antecedent;
(2) Consequent.
§ 212. The Antecedent is the condition on which another
statement is made to depend. It precedes the other in the
order of thought, but may either precede or follow it in
the order of language. Thus we may say indifferently —
' If the wind drops, we shall have rain ' or ' We shall have
rain, if the wind drops.'
§ 213. The Consequent is the statement which is made
subject to some condition.
§ 214. The complex proposition assumes two forms,
(1) If A is B, C is D.
This is known as the Conjunctive or Hypothetical
proposition.
(2) Either A is B or C is D.
62 OF THE DIVISIONS OF PROPOSITIONS.
This is known as the Disjunctive proposition.
§ 215. The disjunctive proposition may also appear in
the form
A is either B or C,
which is equivalent to saying
Either A is B or A is C ;
or again in the form
Either A or B is C,
which is equivalent to saying
Either A is C or B is C.
§ 216. As the double nomenclature may cause some
confusion, a scheme is appended.
Proposition
Simple
(Categorical)
Complex
(Conditional)
1
Conjunctive
(Hypothetical)
Disjunctive.
§ 217. The first set of names is preferable. ' Catego
rical ' properly means ' predicable ' and ' hypothetical '
is a mere synonym for ' conditional/
§ 218. Let us examine now what is the real nature of
the statement which is made in the complex form of pro
position. When, for instance, we say ' If the sky falls, we
shall catch larks/ what is it that we really mean to assert ?
Not that the sky will fall, and not that we shall catch
larks, but a certain connection between the two, namely,
that the truth of the antecedent involves the truth of the
OF THE DIVISIONS OF PROPOSITIONS. 63
consequent. This is why this form of proposition is
called ' conjunctive/ because in it the truth of the con
sequent is conjoined to the truth of the antecedent.
§ 219. Again, when we say 'Jones is either a knave or
a fool/ what is really meant to be asserted is — ' If you do
not find Jones to be a knave, you may be sure that he is
a fool/ Here it is the falsity of the antecedent which
involves the truth of the consequent ; and the proposition
is known as ' disjunctive/ because the truth of the con
sequent is disjoined from the truth of the antecedent.
§ 220. Complex propositions then turn out to be pro
positions about propositions, that is, of which the subject
and predicate are themselves propositions. But the nature
of a proposition never varies in thought. Ultimately every
proposition must assume the form ' A is, or is not, B.'
' If the sky falls, we shall catch larks ' may be compressed
into « Sky-falling is lark-catching.'
§ 221. Hence this division turns upon the form of
expression, and may be said to be founded on the simpli
city or complexity of the terms employed in a proposition.
§ 222. In the complex proposition there appears to be
more than one subject or predicate or both, but in reality
there is only a single statement ; and this statement refers,
as we have seen, to a certain connection between two
propositions.
§ 223. If there were logically, and not merely gram
matically, more than one subject or predicate, there would
be more than one proposition. Thus when we say ' The
Jews and Carthaginians were Semitic peoples and spoke a
64 OF THE DIVISIONS OF PROPOSITIONS.
Semitic language,' we have four propositions compressed
into a single sentence for the sake of brevity.
§ 224. On the other hand when we say ' Either the
Carthaginians were of Semitic origin or argument from
language is of no value in ethnology/ we have two pro
positions only in appearance.
§ 225. The complex proposition then must be distin
guished from those contrivances of language for abbrevi
ating expression in which several distinct statements are
combined into a single sentence.
Verbal and Real Propositions.
§ 226. A Verbal Proposition is one which states no
thing more about the subject than is contained in its
definition, e. g. ' Man is an animal ' ; ' Men are rational
beings.'
§ 227. A Real Proposition states some fact not con
tained in the definition of the subject, e. g. ' Some animals
have four feet/
§ 228. It will be seen that the distinction between verbal
and real propositions assumes a knowledge of the precise
meaning of terms, that is to say, a knowledge of defini
tions.
§ 229. To a person who does not know the meaning
of terms a verbal proposition will convey as much infor
mation as a real one. To say ' The sun is in mid-heaven
at noon,' though a merely verbal proposition, will convey
information to a person who is being taught to attach a
meaning to the word 'noon.' We use so many terms
OF THE DIVISIONS OF PROPOSITIONS. 65
without knowing their meaning, that a merely verbal
proposition appears a revelation to many minds. Thus
there are people who are surprised to hear that the lion is
a cat, though in its definition ' lion ' is referred to the
class ' cat.' The reason of this is that we know material
objects far better in their extension than in their intension,
that is to say, we know what things a name applies to
without knowing the attributes which those things possess
in common.
§ 230. There is nothing in the mere look of a pro
position to inform us whether it is verbal or real ; the
difference is wholly relative to, and constituted by, the
definition of the subject. When we have accepted as the
definition of a triangle that it is 'a figure contained by
three sides,' the statement of the further fact that it has
three angles becomes a real proposition. Again the pro
position ' Man is progressive ' is a real proposition.
For though his progressiveness is a consequence of his
rationality, still there is no actual reference to progressive-
ness contained in the usually accepted definition, ' Man is
a rational animal/
§231. If we were to admit, under the term 'verbal
proposition/ all statements which, though not actually
contained in the definition of the subject, are implied by
it, the whole body of necessary truth would have to be
pronounced merely verbal, and the most penetrating con
clusions of mathematicians set down as only another way
of stating the simplest axioms from which they started.
For the propositions of which necessary truth is composed
F
66 OF THE DIVISIONS OF PROPOSITIONS.
are so linked together that, given one, the rest can always
follow. But necessary truth, which is arrived at ' a priori/
that is, by the mind's own working, is quite as real as
contingent truth, which is arrived at ' a posteriori/ or by the
teachings of experience, in other words, through our own
senses or those of others.
§ 232. The process by which real truth, which is other
than deductive, is arrived at 'a priori' is known as Intuition.
E.g. The mind sees that what has three sides cannot but
have three angles.
§ 233. Only such propositions then must be considered
verbal as state facts expressly mentioned in the definition.
§ 234. Strictly speaking, the division of propositions
into verbal and real is extraneous to our subject : since it
is not the province of logic to acquaint us with the con
tent of definitions.
§ 235. The same distinction as between verbal and real
proposition, is conveyed by the expressions 'Analytical'
and ' Synthetical/ or ' Explicative ' and ' Ampliative/
judgements.
§ 236. A verbal proposition is called analytical, as
breaking up the subject into its component notions.
§ 237. A real proposition is called synthetical, as attach
ing some new notion to the subject.
§ 238. Among the scholastic logicians verbal proposi
tions were known as ' Essential/ because what was stated
in the definition was considered to be of the essence of the
subject, while real propositions were known as 'Accidental/
OF THE DIVISIONS OF PROPOSITIONS. 67
Universal and Particular Propositions.
§ 239. A Universal proposition is one in which it is
evident from the form that the predicate applies to the
subject in its whole extent.
§ 240. When the predicate does not apply to the
subject in its whole extent, or when it is not clear that it
does so, the proposition is called Particular.
§ 241. To say that a predicate applies to a subject in
its whole extent, is to say that it is asserted or denied of
all the things of which the subject is a name.
§ 242. 'All men are mortal' is a universal proposition.
§ 243. 'Some men are black' is a particular proposi
tion. So also is ' Men are fallible ; ' for here it is not
clear from the form whether ' all ' or only ' some ' is
meant.
§ 244. The latter kind of proposition is known as
Indefinite, and must be distinguished from the particular
proposition strictly so called, in which the predicate
applies to part only of the subject.
§ 245. The division into universal and particular is
founded on the Quantity of propositions.
§ 246. The quantity of a proposition is determined by
the quantity in extension of its subject.
§ 247. Very often the matter of an indefinite proposi
tion is such as clearly to indicate to us its quantity.
When, for instance, we say ' Metals are elements/ we are
understood to be referring to all metals ; and the same
thing holds true of scientific statements in general.
F 2
68 OF THE DIVISIONS OF PROPOSITIONS.
Formal logic, however, cannot take account of the matter
of propositions ; and is therefore obliged to set down all
indefinite propositions as particular, since it is not evident
from the form that they are universal.
§ 248. Particular propositions, therefore, are sub-di
vided into such as are Indefinite and such as are Par
ticular, in the strict sense of the term.
§ 249. We must now examine the sub-division of uni
versal propositions into Singular and General.
§ 250. A Singular proposition is one which has a sin
gular term for its subject, e. g. ' Virtue is beautiful/
§ 251. A General proposition is one which has for its
subject a common term taken in its whole extent.
§ 252. Now when we say 'John is a man' or 'This
table is oblong,' the proposition is quite as universal, in
the sense of the predicate applying to the whole of the
subject, as when we say 'All men are mortal/ For
since a singular term applies only to one thing, we
cannot avoid using it in its whole extent, if we use it
at all.
§ 253. The most usual signs of generality in a proposi
tion are the words ' all,' ' every,' ' each/ in affirmative,
and the words 'no,' 'none,' 'not one/ &c. in negative
propositions.
§ 254. The terminology of the division of propositions
according to quantity is unsatisfactory. Not only has
the indefinite proposition to be set down as particular,
even when the sense manifestly declares it to be uni
versal; but the proposition which is expressed in a
OF THE DIVISIONS OF PROPOSITIONS. 69
particular form has also to be construed as indefinite, so
that an unnatural meaning is imparted to the word
' some/ as used in logic. If in common conversation we
were to say * Some cows chew the cud/ the person whom
we were addressing would doubtless imagine us to sup
pose that there were some cows which did not possess
this attribute. But in logic the word ' some ' is not held
to express more than ' some at least, if not all/ Hence
we find not only that an indefinite proposition may, as a
matter of fact, be strictly particular, but that a proposition
which appears to be strictly particular may be indefinite.
So a proposition expressed in precisely the same form
' Some A is B ' may be either strictly particular, if some be
taken to exclude all, or indefinite, if the word ' some '
does not exclude the possibility of the statement being true
of all. It is evident that the term ' particular ' has become
distorted from its original meaning. It would naturally
lead us to infer that a statement is limited to part of the
subject, whereas, by its being opposed to universal, in
the sense in which that term has been defined, it can
only mean that we have nothing to show us whether
part or the whole is spoken of.
§ 255. This awkwardness of expression is due to the
indefinite proposition having been displaced from its
proper position. Formerly propositions were divided
under three heads —
(1) Universal,
(2) Particular,
(3) Indefinite.
70 OF THE DIVISIONS OF PROPOSITIONS.
But logicians anxious for simplification asked, whether
a predicate. in any given case must not either apply to the
whole of the subject or not ? And whether, therefore, the
third head of indefinite propositions were not as super
fluous as the so-called ' common gender ' of nouns in
grammar ?
§ 256. It is quite true that, as a matter of fact, any
given predicate must either apply to the whole of the
subject or not, so that in the nature of things there is no
middle course between universal and particular. But the
important point is that we may not know whether the
predicate applies to the whole of the subject or not.
The primary division then should be into propositions
whose quantity is known and propositions whose quantity
is unknown. Those propositions whose quantity is
known may be sub-divided into ' definitely universal '
and ' definitely particular,' while all those whose quantity
is unknown are classed together under the term ' in
definite/ Hence the proper division is as follows —
Proposition
I I
Definite Indefinite
Universal Particular.
§ 257. Another very obvious defeat of terminology is
that the word ' universal ' is naturally opposed to ' singu
lar,' whereas it is here so used as to include it ; while, on
the other hand, there is no obvious difference between
OF THE DIVISIONS OF PROPOSITIONS. 71
universal and general, though in the division the latter is
distinguished from the former as species from genus.
Affirmative and Negative Propositions.
§ 258. This division rests upon the Quality of proposi
tions.
§ 259. It is the quality of the form to be affirmative or
negative : the quality of the matter, as we saw before
(§ 204), is to be true or false. But since formal logic
takes no account of the matter of thought, when we
speak of ' quality ' we are understood to mean the quality
of the form.
§ 260. By combining the division of propositions ac
cording to quantity with the division according to quality,
we obtain four kinds of proposition, namely —
(1) Universal Affirmative (A).
(2) Universal Negative (E).
(3) Particular Affirmative (I).
(4) Particular Negative (O).
§ 261. This is an exhaustive classification of proposi
tions, and any proposition, no matter what its form may
be, must fall under one or other of these four heads.
For every proposition must be either universal or par
ticular, in the sense that the subject must either be known
to be used in its whole extent or not ; and any proposi
tion, whether universal or particular, must be either
affirmative or negative, for by denying modality to the
copula we have excluded everything intermediate between
downright assertion and denial. This classification there-
72 OF THE DIVISIONS OF PROPOSITIONS.
fore may be regarded as a Procrustes' bed, into which
every proposition is bound to fit at its proper peril.
§ 262. These four kinds of propositions are represented
respectively by the symbols A, E, I, O.
§ 263. The vowels A and I, which denote the two
affirmatives, occur in the Latin words 'affirmo' and
' aio ; ' E and O, which denote the two negatives, occur
in the Latin word ' nego.'
Extensive and Intensive Propositions.
§ 264. It is important to notice the difference between
Extensive and Intensive propositions; but this is not a
division of propositions, but a distinction as to our way
of regarding them. Propositions may be read either in
extension or intension. Thus when we say ' All cows
are ruminants,' we may mean that the class, cow, is con
tained in the larger class, ruminant. This is reading the
proposition in extension. Or we may mean that the
attribute of chewing the cud is contained in, or ac
companies, the attributes which make up our idea of
' cow.' This is reading the proposition in intension. What,
as a matter of fact, we do mean, is a mixture of the two,
namely, that the class, cow, has the attribute of chewing
the cud. For in the ordinary and natural form of pro
position the subject is used in extension, and the predi
cate in intension, that is to say, when we use a subject,
we are thinking of certain objects, whereas when we use
a predicate, we indicate the possession of certain attri
butes. The predicate, however, need not always be used
OF THE DIVISIONS OF PROPOSITIONS. 73
in intension, e. g. in the proposition ' His name is John '
the predicate is not intended to convey the idea of any
attributes at all. What is meant to be asserted is that
the name of the person in question is that particular
name, John, and not Zacharias or Abinadab or any other
name that might be given him.
§ 265. Let it be noticed that when a proposition is
read in extension, the predicate contains the subject,
whereas, when it is read in intension, the subject contains
the predicate.
Exclusive Propositions.
§ 266. An Exclusive Proposition is so called because
in it all but a given subject is excluded from participation
in a given predicate, e. g. ' The good alone are happy/
' None but the brave deserve the fair/ ' No one except
yourself would have done this/
§ 267. By the above forms of expression the predicate
is declared to apply to a given subject and to that subject
only. Hence an exclusive proposition is really equivalent
to two propositions, one affirmative and one negative.
The first of the above propositions, for instance, means
that some of the good are happy, and that no one else is
so. It does not necessarily mean that all the good are
happy, but asserts that among the good will be found all
the happy. It is therefore equivalent to saying that all
the happy are good, only that it puts prominently for
ward in addition what is otherwise a latent consequence
of that assertion, namely, that some at least of the good
are happy.
74 OF THE DIVISIONS OF PROPOSITIONS.
§ 268. Logically expressed the exclusive proposition
when universal assumes the form of an E proposition,
with a negative term for its subject
No not-A is B.
§ 269. Under the head of exclusive comes the strictly
particular proposition, ' Some A is B,' which implies
at the same time that ' Some A is not B.' Here ' some '
is understood to mean ' some only,' which is the meaning
that it usually bears in common language. When, for
instance, we say ' Some of the gates into the park are
closed at nightfall/ we are understood to mean * Some
are left open/
Exceptive Propositions.
§ 270. An Exceptive Proposition is so called as affirm
ing the predicate of the whole of the subject, with the
exception of a certain part, e. g. ' All the jury, except two,
condemned the prisoner/
§ 271. This form of proposition again involves two
distinct statements, one negative and one affirmative,
being equivalent to ' Two of the jury did not condemn
the prisoner ; and all the rest did/
§ 272. The exceptive proposition is merely an affirma
tive way of stating the exclusive —
No not-A is B = All not-A is not-B.
No one but the sage is sane = All except the sage
are mad.
OF THE DIVISIONS OF PROPOSITIONS. 75
Tautologous or Identical Propositions.
§ 273. A Tautologous or Identical proposition affirms
the subject of itself, e. g. ' A man's a man/ ' What I have
written, I have written/ 'Whatever is, is.' The second
of these instances amounts formally to saying ' The thing
that I have written is the thing that I have written/
though of course the implication is that the writing will
not be altered.
CHAPTER IV.
Of the Distribution of Terms.
§ 274. THE treatment of this subject falls under the
second part of logic, since distribution is not an attribute
of terms in themselves, but one which they acquire in
predication.
§ 275. A term is said to be distributed when it is
known to be used in its whole extent, that is, with
reference to all the things of which it is a name. When
it is not so used, or is not known to be so used, it is
called undistributed.
§ 276. When we say ' All men are mortal/ the subject
is distributed, since it is apparent from the form of the
expression that it is used in its whole extent. But when
we say ' Men are miserable ' or * Some men are black/
the subject is undistributed.
§ 277. There is the same ambiguity attaching to the
term 'undistributed' which we found to underlie the use of
the term * particular.' ' Undistributed ' is applied both to a
term whose quantity is undefined, and to one whose quan
tity is definitely limited to a part of its possible extent.
§ 278. This awkwardness arises from not inquiring
first whether the quantity of a term is determined or un
determined, and afterwards proceeding to inquire, whether
OF THE DISTRIBUTION OF TERMS. 77
it is determined as a whole or part of its possible extent.
As it is, to say that a term is distributed, involves two
distinct statements —
(1) That its quantity is known ;
(2) That its quantity is the greatest possible.
The term ' undistributed ' serves sometimes to contradict
one of these statements and sometimes to contradict the
other.
§ 279. With regard to the quantity of the subject of a
proposition no difficulty can arise. The use of the words
' all ' or * some/ or of a variety of equivalent expressions,
mark the subject as being distributed or undistributed re
spectively, while, if there be nothing to mark the quantity,
the subject is for that reason reckoned undistributed.
§ 280. With regard to the predicate more difficulty
may arise.
§ 281. It has been laid down already that, in the
ordinary form of proposition, the subject is used in
extension and the predicate in intension. Let us illus
trate the meaning of this by an example. If someone
were to say * Cows are ruminants/ you would have a
right to ask him whether he meant ' all cows ' or only
' some.' You would not by so doing be asking for fresh
information, but merely for a more distinct explanation
of the statement already made. The subject being used
in extension naturally assumes the form of the whole or
part of a class. But, if you were to ask the same person
' Do you mean that cows are all the ruminants that there
are, or only some of them ? ' he would have a right to
78 OF THE DISTRIBUTION OF TERMS.
complain of the question, and might fairly reply, ' I did
not mean either one or the other ; I was not thinking of
ruminants as a class. I wished merely to assert an attri
bute of cows ; in fact, I meant no more than that cows
chew the cud.'
§ 282. Since therefore a predicate is not used in ex
tension at all, it cannot possibly be known whether it is
used in its whole extent or not.
§ 283. It would appear then that every predicate is
necessarily undistributed; and this consequence does
follow in the case of affirmative propositions.
§ 284. In a negative proposition, however, the predi
cate, though still used in intension, must be regarded as
distributed. This arises from the nature of a negative
proposition. For we must remember that in any pro
position, although the predicate be not meant in exten
sion, it always admits of being so read. Now we cannot
exclude one class from another without at the same time
wholly excluding that other from the former. To take
an example, when we say ' No horses are ruminants/ the
meaning we really wish to convey is that no member of
the class, horse, has a particular attribute, namely, that
of chewing the cud. But the proposition admits of being
read in another form, namely, ' That no member of the
class, horse, is a member of the class, ruminant.' For
by excluding a class from the possession of a given
attribute, we inevitably exclude at the same time any
class of things which possess that attribute from the
former class.
OF THE DISTRIBUTION OF TERMS.
79
§ 285. The difference between the use of a predicate
in an affirmative and in a negative proposition may be
illustrated to the eye as follows. To say ' All A is B '
may mean either that A is included in B or that A and B
are exactly co-extensive.
§ 286. As we cannot be sure which of these two rela
tions of A to B is meant, the predicate B has to be
reckoned undistributed, since a term is held to be distri
buted only when we know that it is used in its whole extent.
§ 287. To say 'No A is B,' however, is to say that A
falls wholly outside of B, which involves the consequence
that B falls wholly outside of A.
§ 288. Let us now apply the same mode of illustration
to the particular forms of proposition.
§ 289. If I be taken in the strictly particular sense,
there are, from the point of view of extension, two things
which may be meant when we say ' Some A is B ' —
8o OF THE DISTRIBUTION OF TERMS.
(i) That A and B are two classes which overlap
one another, that is to say, have some members in
common, e. g. ' Some cats are black.'
(2) That B is wholly contained in A, which is an
inverted way of saying that all B is A, e. g. ' Some
animals are men.'
§ 290. Since we cannot be sure which of these two is
meant, the predicate is again reckoned undistributed.
§ 291. If on the other hand I be taken in an indefinite
sense, so as to admit the possibility of the universal being
true, then the two diagrams which have already been
used for A must be extended to I, in addition to its own,
together with the remarks which we made in connection
with them (§§ 285-6).
§ 292. Again, when we say ' Some A is not B,' we
mean that some, if not the whole of A, is excluded from
the possession of the attribute B. In either case the
OF THE DISTRIBUTION OF TERMS.
8l
things which possess the attribute B are wholly excluded
either from a particular part or from the whole of A.
The predicate therefore is distributed.
From the above considerations we elicit the following —
§ 293. Four Rules for the Distribution of Terms.
(1) All universal propositions distribute their subject.
(2) No particular propositions distribute their sub
ject.
(3) All negative propositions distribute their predicate.
(4) No affirmative propositions distribute their predi
cate.
§ 294. The question of the distribution or non-distribution
of the subject turns upon the quantity of the proposition,
whether universal or particular ; the question of the distri
bution or non-distribution of the predicate turns upon the
quality of the proposition, whether affirmative or negative.
G
CHAPTER V.
Of the Quantification of the Predicate.
§ 295. THE rules that have been given for the dis
tribution of terms, together with the fourfold division of
propositions into A, E, I, O, are based on the assumption
that it is the distribution or non-distribution of the sub
ject only that needs to be taken into account in estimating
the quantity of a proposition.
§ 296. But some logicians have maintained that the
predicate, though seldom quantified in expression, must
always be quantified in thought — in other words, that
when we say, for instance, ' All A is B/ we must mean
either that 'All A is all B' or only that 'All A is
some B.'
§ 297. If this were so, it is plain that the number of
possible propositions would be exactly doubled, and that,
instead of four forms, we should now have to recognise
eight, which may be expressed as follows —
1. All A is all B. (u).
2. All A is some B. (A).
3. No A is any B. (E).
4. No A is some B. (r?).
5. Some A is all B. (Y).
6. Some A is some B. (i).
7. Some A is not any B. (o).
8. Some A is not some B. (»).
OF THE QUANTIFICATION OF THE PREDICATE. 83
§ 298. It is evident that it is the second of the above
propositions which represents the original A, in ac
cordance with the rule that ' No affirmative propositions
distribute their predicate ' (§ 293).
§ 299. The third represents the original E, in^ ac
cordance with the rule that 'All negative propositions
distribute their predicate.'
§ 300. The sixth represents the original I, in ac
cordance with the rule that ' No affirmative propositions
distribute their predicate.'
§ 301. The seventh represents the original O, in ac
cordance with the rule that 'All negative propositions
distribute their predicate.'
§ 302. Four new symbols are required, if the quantity
of the predicate as well as that of the subject be taken
into account in the classification of propositions. These
have been supplied, somewhat fancifully, as follows —
§ 303. The first, ' All A is all B,' which distributes
both subject and predicate, has been called u, to mark its
extreme universality.
§ 304. The fourth, ' No A is some B/ is contained in
E, and has therefore been denoted by the symbol y, to
show its connection with E.
§ 305. The fifth, 'Some A is all B,' is the exact con
verse of the second, ' All A is some B/ and has therefore
been denoted by the symbol Y, which resembles an in
verted A.
§ 306. The eighth is contained in O, as part in whole,
and has therefore had assigned to it the symbol o>.
G 2
84 OF THE QUANTIFICATION OF THE PREDICATE.
§ 307. The. attempt to take the predicate in extension,
instead of, as it should naturally be taken, in intension,
leads to some curious results. Let us take, for instance,
the u proposition. Either the sign of quantity ' all ' must
be understood as forming part of the predicate or not.
If it is not, then the u proposition ' All A is all B ' seems
to contain within itself, not one proposition, but two,
namely, 'All A is B ' and ' All B is A.' But if on the
other hand ' all ' is understood to form part of the predi
cate, then u is not really a general but a singular pro
position. When we say, ' All men are rational animals/
we have a true general proposition, because the predicate
applies to the subject distributively, and not collectively.
What we mean is that ' rational animal ' may be affirmed
of every individual in the class, man. But when we say
' All men are all rational animals,' the predicate no longer
applies to the subject distributively, but only collectively.
For it is obvious that 'all rational animals' cannot be
affirmed of every individual in the class, man. What the
proposition means is that the class, man, is co-extensive
with the class, rational animal. The same meaning may
be expressed intensively by saying that the one class has
the attribute of co-extension with the other.
§ 308. Under the head o u come all propositions in
which both subject and predicate are singular terms,
e.g. 'Homer was the author of the Iliad/ 'Virtue is the
way to happiness.'
§ 309. The proposition 77 conveys very little information
to the mind. ' No A is some B ' is compatible with the
OF THE QUANTIFICATION OF THE PREDICATE. 85
A proposition in the same matter. ' No men are some
animals' may be true, while at the same time it is true that
'All men are animals/ No men, for instance, are the
particular animals known as kangaroos.
§ 310. The w proposition conveys still less information
than the 77. For o> is compatible, not only with A, but
with u. Even though ' All men are all rational animals/
it is still true that ' Some men are not some rational
animals ' : for no given human being is the same rational
animal as any other.
§ 311. Nay, even when the u is an identical proposition,
o> will still hold in the same matter. ' All rational animals
are all rational animals ' : but, for all that, ' Some rational
animals are not some others/ This last form of proposi
tion therefore is almost wholly devoid of meaning.
§ 312. The chief advantage claimed for the quantifica
tion of the predicate is that it reduces every affirmative
proposition to an exact equation between its subject and
predicate. As a consequence every proposition would
admit of simple conversion, that is to say, of having the
subject and predicate transposed without any further
change in the proposition. The forms also of Reduction
(a term which will be explained later on) would be
simplified ; and generally the introduction of the quantified
predicate into logic might be attended with certain
mechanical advantages. The object of the logician,
however, is not to invent an ingenious system, but to
arrive at a true analysis of thought. Now, if it be
admitted that in the ordinary form of proposition the
86 OP THE QUANTIFICATION OF THE PREDICATE.
subject is used in extension and the predicate in intension,
the ground for the doctrine is at once cut away. For, if
the predicate be not used in its extensive capacity at all,
we plainly cannot be called upon to determine whether it
is used in its whole extent or not.
CHAPTER VI.
Of the Heads of Predicables.
§ 313. A PREDICATE is something which is stated of a
subject.
§ 314. A predicable is something which can be stated
of a subject.
§ 315. The Heads of Predicables are a classification of
the various things which can be stated of a subject,
viewed in their relation to it.
§ 316. The treatment of this topic, therefore, as it
involves the relation of a predicate to a subject, manifestly
falls under the second part of logic, which deals with the
proposition. It is sometimes treated under the first part
of logic, as though the heads of predicables were a
classification of universal notions, i.e. common terms, in
relation to one another, without reference to their place in
the proposition.
§ 317. The heads of predicables are commonly reckoned
as five, namely,
(1) Genus.
(2) Species.
(3) Difference.
(4) Property.
(5) Accident.
§ 318. We will first define these terms in the sense in
88 OF THE HEADS OF PREDICABLES.
which they are now used, and afterwards examine the
principle on which the classification is founded and the
sense in which they were originally intended.
(1) A Genus is a larger class containing under it
smaller classes. Animal is a genus in relation
to man and brute.
(2) A Species is a smaller class contained under a
larger one. Man is a species in relation to
animal.
(3) Difference is the attribute, or attributes, which
distinguish one species from others contained
under the same genus. Rationality is the attri
bute which distinguishes the species, man, from
the species, brute.
N.B. The genus and the difference together
make up the Definition of a class-name, or
common term.
(4) A Property is an attribute which is not contained
in the definition of a term, but which flows
from it.
A Generic Property is one which flows from
the genus.
A Specific Property is one which flows from
the difference.
It is a generic property of man that he is
mortal, which is a consequence of his animality.
It is a specific property of man that he is pro
gressive, which is a consequence of his ration
ality.
OF THE HEADS OF PREDICABLES. 89
(5) An Accident is an attribute, which is neither
contained in the definition, nor flows from it.
§ 319. Accidents are either Separable or Inseparable.
A Separable Accident is one which belongs only to some
members of a class.
An Inseparable Accident is one which belongs to all
the members of a class.
Blackness is a separable accident of man, an inseparable
accident of coals.
§ 320. The attributes which belong to anything may
be distinguished broadly under the two heads of essential
and non-essential, or accidental. By the essential attributes
of anything are meant those which are contained in, or
which flow from, the definition. Now it may be questioned
whether there can, in the nature of things, be such a thing
as an inseparable accident. For if an attribute were
found to belong invariably to all the members of a class,
we should suspect that there was some causal connection
between it and the attributes which constitute the defini
tion, that is, we should suspect the attribute in question
to be essential and not accidental. Nevertheless the term
' inseparable accident ' may be retained as a cloak for our
ignorance, whenever it is found that an attribute does, as
a matter of fact, belong to all the members of a class,
without there being any apparent reason why it should do
so. It has been observed that animals which have horns
chew the cud. As no one can adduce any reason why
animals that have horns should chew the cud any more
than animals which have not, we may call the fact of
90 OF THE HEADS OF PREDICABLES.
chewing the cud an inseparable accident of horned
animals.
§ 321. The distinction between separable and in
separable accidents is sometimes extended from classes to
individuals.
An inseparable accident of an individual is one which
belongs to him at all times. A separable accident of an
individual is one which belongs to him at one time and
not at another.
§ 322. It is an inseparable accident of an individual
that he was born at a certain place and on a certain date.
It is a separable accident of an individual that he resides
at a certain place and is of a certain age.
§ 323. There are some remarks which it may be well to
make about the above five terms before we pass on to
investigate the principle upon which the division is based.
§ 324. In the first place, it must of course be borne in
mind that genus and species are relative terms. No class
in itself can be either a genus or a species; it only
becomes so in reference to some other class, as standing
to it in the relation of containing or contained.
§ 325. Again, the distinction between genus and differ
ence on the one hand and property on the other is wholly
relative to an assumed definition. When we say ' Man is
an animal/ ' Man is rational/ * Man is progressive/
there is nothing in the nature of these statements them
selves to tell us that the predicate is genus, difference, or
property respectively. It is only by a tacit reference to
the accepted definition of man that this becomes evident
OF THE HEADS OF PREDICABLES. 91
to us. Similarly, we cannot know beforehand that the
fact of a triangle having three sides is its difference, and
the fact of its having three angles a property. It is only
when we assume the definition of a triangle as a three-
sided figure that the fact of its having three angles sinks
into a property. Had we chosen to define it, in accord
ance with its etymological meaning, as a figure with three
angles, its three-sidedness would then have been a mere
property, instead of being the difference ; for these two
attributes are so connected together that, whichever is
postulated, the other will necessarily follow.
§ 326. Lastly, it must be noticed that we have not
really defined the term ' accident,' not having stated what
it is, but only what it is not. It has in fact been reserved
as a residual head to cover any attribute which is neither
a difference nor a property.
§ 327. If the five heads of predicables above given were
offered to us as an exhaustive classification of the possible
relations in which the predicate can stand to the subject
in a proposition, the first thing that would strike us is that
they do not cover the case in which the predicate is a sing
ular term. In such a proposition as ' This man is John/
we have neither a predication of genus or species nor of
attribute : but merely the identification of one term with
another, as applying to the same object. Such criticism
as this, however, would be entirely erroneous, since no
singular term was regarded as a predicate. A predicable
was another name for a universal, the common term being
called a predicable in one relation and a universal in
92 OF THE HEADS OF PREDICABLES.
another — a predicable, extensively, in so far as it was
applicable to several different things, a universal, inten
sively, in so far as the attributes indicated were implied
in several other notions, as the attributes indicated by
' animal ' are implied in ' horse/ ' sheep,' ' goat/ &c.
§ 328. It would be less irrelevant to point out how the
classification breaks down in relation to the singular term
as subject. When, for instance, we say ' Socrates is an
animal/ ' Socrates is a man/ there is nothing in the pro
position to show us whether the predicate is a genus or a
species : for we have not here the relation of class to class,
which gives us genus or species according to their relative
extension, but the relation of a class to an individual.
§ 329. Again, when we say
(1) Some animals are men,
(2) Some men are black,
what is there to tell us that the predicate is to be
regarded in the one case as a species and in the other
as an accident of the subject ? Nothing plainly but the
assumption of a definition already known.
§ 330. But if this assumption be granted, the classifica
tion seems to admit of a more or less complete defense by
logic.
For, given any subject, we can predicate of it either a
class or an attribute.
When the predicate is a class, the term predicated is
called a Genus, if the subject itself be a class, or a
Species, if it be an individual.
When, on the other hand, the predicate is an attribute,
OF THE HEADS OF PREDICABLES. 93
the attribute predicated may be either the very attribute
which distinguishes the subject from other members of the
same class, in which case it is called the Difference, or it
may be some attribute connected with the definition, i.e.
Property, or not connected with it, i.e. Accident.
§ 331. These results may be exhibited in the following
scheme —
Predicate
Class
|
Attri
bute
(Subject a
common
term)
Genus
(Subject a
singular
term)
Species
(The
distinguishing
attribute)
Difference
' (Nc
disting
attr
t the
••uishing
bute)
(Connected
with the
definition)
Property
(Not connected
with the
definition)
Accident.
§ 332. The distinction which underlies this division
between predicating a class and predicating an attribute
(in quid or in quale) is a perfectly intelligible one,
corresponding as it does to the grammatical distinction
between the predicate being a noun substantive or a noun
adjective. Nevertheless it is a somewhat arbitrary one,
since, even when the predicate is a class-name, what we
are concerned to convey to the mind, is the fact that the
subject possesses the attributes which are connoted by
that class-name. We have not here the difference be
tween extensive and intensive predication, since, as we
have already seen (§ 264), that is not a difference between
94 OP THE HEADS OF PREDICABLES.
one proposition and another, but a distinction in our
mode of interpreting any and every proposition. What
ever proposition we like to take may be read either in
extension or in intension, according as we fix our minds
on the fact of inclusion in a class or the fact of the
possession of attributes.
§ 333. It will be seen that the term 'species/ as it
appears in the scheme, has a wholly different meaning
from the current acceptation in which it was defined
above. Species, in its now accepted meaning, signifies
the relation of a smaller class to a larger one : as it was
originally intended in the heads of predicables it signifies
a class in reference to individuals.
§ 334. Another point which requires to be noticed with
regard to this five-fold list of heads of predicables, if its
object be to classify the relations of a predicate to a
subject, is that it takes no account of those forms of
predication in which class and attribute are combined.
Under which of the five heads would the predicates in the
following propositions fall ?
(1) Man is a rational animal.
(2) Man is a featherless biped.
In the one case we have a combination of genus and
difference ; in the other we have a genus combined with
an accident.
§ 335. The list of heads of predicables which we have
been discussing is not derived from Aristotle, but from the
' Introduction ' of Porphyry, a Greek commentator who
lived more than six centuries later.
OF THE HEADS OF PREDICABLES. 95
Aristotle s Heads of Predicates.
§ 336. Aristotle himself, by adopting a different basis
of division, has allowed room in his classification for the
mixed forms of predication above alluded to. His list
contains only four heads, namely,
Genus (yeW).
Definition
Proprium
Accident
§ 337. Genus here is not distinguished from difference.
Whether we say ' Man is an animal ' or ' Man is rational/
we are equally understood to be predicating a genus.
§ 338. There is no account taken of species, which,
when predicated, resolves itself either into genus or
accident. When predicated of an individual, it is re
garded as a genus, e.g. 'Socrates is a man'; when
predicated of a class, it is regarded as an accident, e.g.
' Some animals are men.'
§ 339. Aristotle's classification may easily be seen to
be exhaustive. For every predicate must either be co
extensive with its subject or not, i. e. predicable of the same
things. And if the two terms coincide in extension, the
predicate must either coincide also in intension with the
subject or not.
A predicate which coincides both in extension and
intension with its subject is exactly what is meant by a
definition. One which coincides in extension without
coinciding in intension, that is, which applies to the same
g6 OF THE HEADS OF PREDICABLES.
things without expressing the whole meaning of the
subject, is what is known as a Proprium or Peculiar
Property.
If, on the other hand, the two terms are not co-extensive,
the predicate must either partially coincide in intension
with the subject or not1. This is equivalent to saying
that it must either state part of the definition of the subject
or not. Now the definition is made up of genus and
difference, either of which may form the predicate : but as
the two are indistinguishable in relation to a single subject,
they are lumped together for the present purpose under
the one head, genus. When the predicate, not being
co-extensive, is not even partially co-intensive with its
subject, it is called an Accident.
§ 340. Proprium, it will be seen, differs from property.
A proprium is an attribute which is possessed by all
the members of a class, and by them alone, e. g. * Men
are the only religious animals/
§ 341. Under the head of definition must be included
all propositions in which the predicate is a mere synonym
of the subject, e. g. * Naso is Ovid/ ' A Hebrew is a Jew/
' The skipper is the captain/ In such propositions the
predicate coincides in extension with the subject, and may
be considered to coincide in intension where the intension
1 The case could not arise of a predicate which was entirely co
incident in intension with a subject with which it was not co-exten
sive. For, if the extension of the predicate were greater than that of
the subject, its intension would be less, and if less, greater, in
accordance with the law of inverse variation of the two quantities
(§ 166).
OF THE HEADS OF PREDICABLES. 97
of both subject and predicate is at zero, as in the case of
two proper names.
§ 342. Designations and descriptions will fall under
the head of ' proprium ' or peculiar property, e. g. ' Lord
Salisbury is the present prime minister of England/ ' Man
is a mammal with hands and without hair/ For here,
while the terms are coincident in extension, they are far
from being so in intension.
§ 343. The term ' genus ' must be understood to in
clude not only genus in the accepted sense, but difference
and generic property as well.
§ 344. These results may be exhibited in the following
scheme —
Predicate
I
Coextensive with the subject not coextensive
Cointensive with not cointensive partially cointensive not at all
the subject
6pi.crju.6s iSiov yeVo? o-i>/uj3ej3r)K(k
J | Accident
I I I I I -I I I
Definition Synonym Designa- Descrip- Peculiar Genus Differ- Generic
tion tion Property ence Property.
§ 345. Thus Aristotle's four heads of predicables may
be split up, if we please, into nine —
1. Definition \
2. Synonym J '
3. Designation \
4. Description >i'§ioi/.
5. Peculiar Property J
98 OF THE HEADS OF PREDICABLES.
6. Genus ^
7. Difference VyeW.
8. Generic Property J
9. Accident — av^f^Kos.
§ 346. We now pass on to the two subjects of Defini
tion and Division, the discussion of which will complete
our treatment of the second part of logic. Definition
and division correspond respectively to the two kinds of
quantity possessed by terms.
Definition is unfolding the quantity of a term in in
tension.
Division is unfolding the quantity of a term in extension.
CHAPTER VII.
Of Definition.
§ 347. To define a term is to unfold its intension,
i. e. to explain its meaning.
§ 348. From this it follows that any term which
possesses no intension cannot be defined.
§ 349. Hence proper names do not admit of definition,
except just in so far as they do possess some slight degree
of intension. Thus we can define the term ' John ' only
so far as to say that c John ' is the name of a male person.
This is said with regard to the original intension of proper
names ; their acquired intension will be considered later.
§ 350. Again, since definition is unfolding the intension
of a term, it follows that those terms will not admit of
being defined whose intension is already so simple that it
cannot be unfolded further. Of this nature are names of
simple attributes, such as greenness, sweetness, pleasure,
existence. We know what these things are, but we
cannot define them. To a man who has never enjoyed
sight, no language can convey an idea of the greenness of
the grass or the blueness of the sky; and if a person were
unaware of the meaning of the term ' sweetness/ no form
of words could convey to him an idea of it. We might
put a lump of sugar into his mouth, but that would not be
a logical definition.
H 2
100 OF DEFINITION.
§ 351. Thus \ve see that, for a thing to admit of
definition, the idea of it must be complex. Simple ideas
baffle definition, but at the same time do not require it.
In defining we lay out the simpler ideas which are com
bined in our notion of something, and so explain that
complex notion. We have defined 'triangle,' when we
analyse it into ' figure ' and ( contained by three lines.'
Similarly we have defined ' substance ' when we analyse it
into ' thing ' and ' which can be conceived to exist by
itself.'
§ 352. But when we get to 'thing' we have reached a
limit. The Summum Genus, or highest class under
which all things fall, cannot be defined any more than a
simple attribute ; and for the very good reason that it
connotes nothing but pure being, which is the simplest of
all attributes. To say that a thing is an ' object of
thought ' is not really to define it, but to explain its
etymology, and to reclaim a philosophical term from its
abuse by popular language, in which it is limited to the
concrete and the lifeless. Again, to define it negatively
and to say that a thing is ' that which is not nothing ' does
not carry us any further than we were before. The law
of contradiction warrants us in saying as much as that.
§ 353. Definition is confined to subject-terms, and does
not properly extend to attributives. For definition is of
things through names, and an attributive out of predica
tion is not the name of anything. The attributive is
defined, so far as it can be, through the corresponding
abstract term.
OF DEFINITION. IOI
§ 354. Common terms, other than attributives, ought
always to admit of definition. For things are distributed
by the mind into classes owing to their possessing certain
attributes in common, and the definition of the class-
name can be effected by detailing these attributes, or at
least a sufficient number of them.
§ 355. It is different with singular terms. Singular
terms, when abstract, admit of definition, in so far as they
are not names of attributes so simple as to evade analysis.
When singular terms are concrete, we have to distinguish
between the two cases of proper names and designations.
Designations are connotative singular terms. They are
formed by limiting a common term to the case in hand.
Whatever definition therefore fits the common term will
fit also the designation which is formed from it, if we add
the attributes implied by the limitations. Thus whatever
definition fits the common term ' prime minister ' will fit
also the singular term ' the present prime minister of
England ' by the addition to it of the attributes of place
and time which are indicated by the expression. Such
terms as this have a definite amount of intension, which
can therefore be seized upon and expounded by a
definition.
§ 356. But proper names, having no original intension
of their own, cannot be defined at all ; whereas, if we look
upon them from the point of view of their acquired inten
sion, they defy definition by reason of the very complexity
of their meaning. We cannot say exactly what ' John '
and ' Mary ' mean, because those names, to us who know
102 OF DEFINITION.
the particular persons denoted by them, suggest all the
most trifling accidents of the individual as well as the
essential attributes of the genus.
§ 357. Definition serves the practical purpose of enabling
us mentally to distinguish, or, as the name implies, * mark
off' the thing defined from all other things whatsoever.
This may seem at first an endless task, but there is a
short cut by which the goal may be reached. For, if
we distinguish the thing in hand from the things which it
is most like, we shall, 'a fortiori,' have distinguished it
from things to which it bears a less resemblance.
§ 358. Hence the first thing to do in seeking for a
definition is to fix upon the class into which the thing to
be defined most naturally falls, and then to distinguish the
thing in question from the other members of that class.
If we were asked to define a triangle, we would not begin
by distinguishing it from a hawser, but from a square
and other figures with which it is more possible to con
found it. The class into which a thing falls is called its
Genus, and the attribute or attributes which distinguish it
from other members of that class are called its Difference.
§ 359. If definition thus consists in referring a thing to
a class, we see a further reason why the summum genus
of all things cannot be defined.
§ 360. We have said that definition is useful in enabling
us to distinguish things from one another in our minds :
but this must not be regarded as the direct object of the
process. For this object may be accomplished without
giving a definition at all, by means of what is called a
OF DEFINITION. 103
Description. By a description is meant an enumeration
of accidents with or without the mention of some class-
name. It is as applicable to proper names as to common
terms. When we say ' John Smith lives next door on the
right-hand side and passes by to his office every morning
at nine o'clock,' we have, in all probability, effectually
distinguished John Smith from other people : but living
next, &c., cannot be part of the intension of John Smith,
since John Smith may change his residence or abandon
his occupation without ceasing to be called by his name.
Indirectly then definition serves the purpose of dis
tinguishing things in the mind, but its direct object is to
unfold the intension of terms, and so impart precision to
our thoughts by setting plainly before us the meaning of
the words we are using.
§ 361. But when we say that definition is unfolding the
intension of terms, it must not be imagined that we are
bound in defining to unfold completely the intension of
terms. This would be a tedious, and often an endless,
task. A term may mean, or convey to the mind, a good
many more attributes than those which are stated in
its definition. There is no limit indeed to the meaning
which a term may legitimately convey, except the common
attributes of the things denoted by it. Who shall say, for
instance, that a triangle means a figure with three sides,
and does not mean a figure with three angles, or the sur
face of the perpendicular bisection of a cone ? Or again,
that man means a rational, and does not mean a speaking,
a religious, or an aesthetic animal, or a biped with two
104 OF DEFINITION.
eyes, a nose, and a mouth ?• The only attributes of which
it can safely be asserted that they can form no part of the
intension of a term are those which are not common to
all the things to which the name applies. Thus a
particular complexion, colour, height, creed, nationality
cannot form any part of the intension of the term c man.'
But among the attributes common to a class we cannot
distinguish between essential and unessential, except by
the aid of definition itself. Formal logic cannot recognise
any order of priority between the attributes common to
all the members of a class, such as to necessitate our re
cognising some as genera and differentiae and relegating
others to the place of properties or inseparable accidents.
§ 362. The art of giving a good definition is to seize
upon the salient characteristics of the thing defined and
those wherefrom the largest number of other attributes
can be deduced as consequences. To do this well re
quires a special knowledge of the thing in question, and is
not the province of the formal logician.
§ 363. We have seen already, in treating of the Heads
of Predicables (§ 325), that the difference between genus
and difference on the one hand and property on the
other is wholly relative to some assumed definition. Now
definitions are always to a certain extent arbitrary, and
will vary with the point of view from which we consider
the thing required to be defined. Thus ' man ' is usually
contrasted with ' brute/ and from this point of view it is
held a sufficient definition of him to say that he is ' a
rational animal.' But a theologian might be more
OF DEFINITION.
105
anxious to contrast man with supposed incorporeal in
telligences, and from this point of view man would be
defined as an ' embodied spirit/
§ 364. In the two definitions just given it will be
noticed that we have really employed exactly the same
attributes, only their place as genus and difference has
been reversed. It is man's rational, or spiritual, nature
which distinguishes him from the brutes : but this is just
what he is supposed to have in common with incorporeal
intelligences, from whom he is differentiated by his
animal nature.
This illustration is sufficient to show us that, while
there is no absolute definition of anything, in the sense of
a fixed genus and difference, there may at the same time
be certain attributes which permanently distinguish the
members of a given class from those of all other classes.
§ 365. The above remarks will have made it clear that
the intension of a term is often much too wide to be
conveyed by any definition ; and that what a definition
generally does is to select certain attributes from the
whole intension, which are regarded as being more typical
of the thing than the remainder. No definition can be
expected to exhaust the whole intension of a term, and
106 OF DEFINITION.
there will always be room for varying definitions of the
same thing, according to the different points of view from
which it is approached.
§ 366. Names of attributes lend themselves to definition
far more easily than names of substances. The reason of
this is that names of attributes are primarily intensive in
force, whereas substances are known to us in extension
before they become known to us in intension. There
is no difficulty in defining a term like c triangle ' or
' monarchy,' because these terms were expressly invented
to cover certain attributes ; but the case is different with
such terms as ' dog/ ' tree/ ' plant/ ' metal/ and other
names of concrete things. We none of us have any
difficulty in recognising a dog or tree, when we see them,
or in distinguishing them from other animals or plants
respectively. We are therefore led to imagine that we
know the meaning of these terms. It is not until we are
called upon for a definition that we discover how super
ficial our knowledge really is of the common attributes
possessed by the things which these names denote.
§ 367. It might be imagined that a common name
would never be given to things except in virtue of our
knowledge of their common attributes. But as a matter
of fact, the common name was first given from a confused
notion of resemblance, and we had afterwards to detect
the common attributes, when sometimes the name had
been so extended from one thing to another like it, that
there were hardly any definite attributes possessed in
common by the earlier and later members of the class.
OF DEFINITION. 1 07
§ 368. This is especially the case where the meaning of
terms has been extended by analogy, e. g. head, foot, arm,
post, pole, pipe, &c.
§ 369. But in the progress of thought we come to form
terms in which the intensive capacity is everything. Of
this kind notably are mathematical conceptions. Terms
of this kind, as we said before, lend themselves readily to
definition.
§ 370. We may lay down then roughly that words are
easy or difficult of definition according as their intensive
or extensive capacity predominates.
§ 371. There is a marked distinction to be observed
between the classes made by the mind of man and the
classes made by nature, which are known as ' real kinds.'
In the former there is generally little or nothing in
common except the particular attribute which is selected
as the ground of classification, as in the case of red and
white things, which are alike only in their redness or
whiteness ; or else their attributes are all necessarily con
nected, as in the case of circle, square and triangle. But
the members of nature's classes agree in innumerable
attributes which have no discoverable connection with one
another, and which must therefore, provisionally at least,
be regarded as standing in the relation of inseparable
accidents to any particular attributes which we may select
for the purposes of definition. There is no assignable
reason why a rational animal should have hair on its
head or a nose on its face, and yet man, as a matter
of fact, has both ; and generally the particular bodily
108 OF DEFINITION.
configuration of man can only be regarded as an in
separable accident of his nature as a rational animal.
§ 372. ' Real kinds' belong to the class of words
mentioned above in which the extension predominates
over the intension. We know well enough the things
denoted by them, while most of us have only a dim
idea of the points of resemblance between these things.
Nature's classes moreover shade off into one another by
such imperceptible degrees that it is often impossible to
fix the boundary line between one class and another. A
still greater source of perplexity in dealing with real kinds
is that it is sometimes almost impossible to fix upon any
attribute which is common to every individual member of
the class without exception. All that we can do in such
cases is to lay down a type of the class in its perfect form,
and judge of individual instances by the degree of their
approximation to it. Again, real kinds being known to us
primarily in extension, the intension which we attach to
the names is liable to be affected by the advance of know
ledge. In dealing therefore with such terms we must
be content with provisional definitions, which adequately
express our knowledge of the things denoted by them, at
the time, though a further study of their attributes may
induce us subsequently to alter the definition. Thus the
old definition of animal as a sentient organism has been
rendered inadequate by the discovery that so many of the
phenomena of sensation can be exhibited by plants.
§ 373. But terms in which intension is the predominant
idea are more capable of being defined once for all.
OF DEFINITION. 109
Aristotle's definitions of ' wealth ' and ' monarchy ' are as
applicable now as in his own day, and no subsequent
discoveries of the properties of figures will render Euclid's
definitions unavailable.
§ 374. We may distinguish therefore between two kinds
of definition, namely,
(1) Final.
(2) Provisional.
§ 375. A distinction is also observed between Real and
Nominal Definitions. Both of these explain the meaning
of a term : but a real definition further assumes the
actual existence of the thing defined. Thus the explana
tion of the term ' Centaur' would be a nominal, that of
' horse ' a real definition.
It is useless to assert, as is often done, that a nominal
definition explains the meaning of a term and a real
definition the nature of a thing ; for, as we have seen
already, the meaning of a term is whatever we know of
the nature of a thing.
§ 376. It now remains to lay down certain rules for
correct definition.
§ 377. The first rule that is commonly given is that a
definition should state the essential attributes of the thing
defined. But this amounts merely to saying that a defini
tion should be a definition ; since it is only by the aid of
definition that we can distinguish between essential and
non-essential among the common attributes exhibited by
a class of things. The rule however may be retained as a
material test of the soundness of a definition, in the sense
110 OF DEFINITION.
that he who seeks to define anything should fix upon its
most important attributes. To define man as a mammi-
ferous animal having two hands, or as a featherless biped,
we feel to be absurd and incongruous, since there is
no reference to the most salient characteristic of man,
namely, his rationality. Nevertheless we cannot quarrel
with these definitions on formal, but only on material
grounds. Again, if anyone chose to define logic as the
art of thinking, all we could say is that we differ from
him in opinion, as we think logic is more properly to be
regarded as the science of the laws of thought. But here
also it is on material grounds that we dissent from the
definition.
§ 378. Confining ourselves therefore to the sphere
with which we are properly concerned, we lay down the
following
Rules for Definition.
(1) A definition must be co-extensive with the term
defined.
(2) A definition must not state attributes which imply
one another.
(3) A definition must not contain the name defined,
either directly or by implication.
(4) A definition must be clearer than the term
defined.
(5) A definition must not be negative, if it can be
affirmative.
Briefly, a definition must be adequate (i), terse (2),
OF DEFINITION. 1 1 1
clear (4); and must not be tautologous (3), or, if it can be
avoided, negative (5).
§ 379. It is worth while to notice a slight ambiguity in
the term ' definition ' itself. Sometimes it is applied to
the whole proposition which expounds the meaning of the
term ; at other times it is confined to the predicate of this
proposition. Thus in stating the first four rules we have
used the term in the latter sense, and in stating the fifth in
the former.
§ 380. We will now illustrate the force of the above
rules by giving examples of their violation.
Rule i. Violations. A triangle is a figure with
three equal sides.
A square is a four-sided figure having all its sides
equal.
In the first instance the definition is less extensive than
the term defined, since it applies only to equilateral
triangles. This fault may be amended by decreasing the
intension, which we do by eliminating the reference to the
equality of the sides.
In the second instance the definition is more extensive
than the term defined. We must accordingly increase the
intension by adding a new attribute * and all its angles
right angles.'
Rule 2. Violation. A triangle is a figure with
three sides and three angles.
One of the chief merits of a definition is to be terse, and
this definition is redundant, since what has three sides
cannot but have three angles.
112 OF DEFINITION.
Rule 3. Violations. A citizen is a person both of
whose parents were citizens.
Man is a human being.
Rule 4. Violations. A net is a reticulated fabric,
decussated at regular intervals.
Life is the definite combination of heterogeneous
changes, both simultaneous and successive, in
correspondence with external co-existences and
sequences.
Rule 5. Violations. A mineral is that which is
neither animal nor vegetable.
Virtue is the absence of vice.
§ 381. The object of definition being to explain what
a thing is, this object is evidently defeated, if we confine
ourselves to saying what it is not. But sometimes this is
impossible to be avoided. For there are many terms
which, though positive in form, are privative in force.
These terms serve as a kind of residual heads under
which to throw everything within a given sphere, which
does not exhibit certain positive attributes. Of this un
avoidably negative nature was the definition which we
give of ' accident,' which amounted merely to saying that
it was any attribute which was neither a difference nor a
property.
§ 382. The violation of Rule 3, which guards against
defining a thing by itself, is technically known as 'circulus
in definiendo/ or defining in a circle. This rule is often
apparently violated, without being really so. Thus Euclid
defines an acute-angled triangle as one which has three
OF DEFINITION. 113
acute angles. This seems a glaring violation of the rule,
but is perfectly correct in its context ; for it has already
been explained what is meant by the terms ' triangle '
and ' acute angle,' and all that is now required is to dis
tinguish the acute-angled triangle from its cognate species.
He might have said that an acute-angled triangle is one
which has neither a right angle nor an obtuse angle : but
rightly preferred to throw the same statement into a
positive form.
§ 383. The violation of Rule 4 is known as ' ignotum
per ignotius' or 'per aeque ignotum.' This rule also
may seemingly be violated when it is not really so. For
a definition may be correct enough from a special point of
view, which, apart from that particular context, would
appear ridiculous. From the point of view of conic
sections, it is correct enough to define a triangle as that
section of a cone which is formed by a plane passing
through the vertex perpendicularly to the base, but this
could not be expected to make things clearer to a person
who was inquiring for the first time into the meaning of
the word triangle. But a real violation of the fourth rule
may arise, not only from obscurity, but from the employ
ment of ambiguous language or metaphor. To say that
' temperance is a harmony of the soul/ or that ' bread is
the staff of life,' throws no real light upon the nature of
the definiend.
§ 384. The material correctness of a definition is, as
we have already seen, a matter extraneous to formal
logic. An acquaintance with the attributes which terms
i
114 OF DEFINITION.
imply involves material knowledge quite as much as an
acquaintance with the things they apply to ; knowledge of
the intension and of the extension of terms is alike
acquired by experience. No names are such that their
meaning is rendered evident by the very constitution of
our mental faculties ; yet nothing short of this would
suffice to bring the material content of definition within
the province of formal logic.
CHAPTER VIII.
Of Division.
§ 385. To divide a term is to unfold its extension, that
is, to set forth the things of which it is a name.
§ 386. But as in definition we need not completely
unfold the intension of a term, so in division we must not
completely unfold its extension.
§ 387. Completely to unfold the extension of a term
would involve stating all the individual objects to which
the name applies, a thing which would be impossible in
the case of most common terms. When it is done, it is
called Enumeration. To reckon up all the months of the
year from January to December would be an enumera
tion, and not a division, of the term ' month.'
§ 388. Logical division always stops short at classes.
It may be defined as the statement of the various classes
of things that can be called by a common name. Tech
nically we may say that it consists in breaking up a genus
into its component species.
§ 389. Since division thus starts with a class and ends
with classes, it is clear that it is only common terms
which admit of division, and also that the members of the
division must themselves be common terms.
§ 390. An ' individual ' is so called as not admitting of
I 2
Il6 OF DIVISION.
logical division. We may divide the term ' cow ' into
classes, as Jersey, Devonshire, &c., to which the name
' cow ' will still be applicable, but the parts of an in
dividual cow are no longer called by the name of the
whole, but are known as beefsteaks, briskets, &c.
§ 391. In dividing a term the first requisite is to fix
upon some point wherein certain members of the class
differ from others. The point thus selected is called the
Fundamentum Divisionis or Basis of the Division.
§ 392. The basis of the division will of course differ
according to the purpose in hand, and the same term will
admit of being divided on a number of different principles.
Thus we may divide the term 'man,' on the basis of
colour, into white, black, brown, red, and yellow ; or, on
the basis of locality, into Europeans, Asiatics, Africans,
Americans, Australians, New Zealanders, and Polynesians ;
or again, on a very different principle, into men of
nervous, sanguine, bilious, lymphatic and mixed tempera
ments.
§ 393. The term required to be divided is known as
the Totum Divisum or Divided Whole. It might also
be called the Dividend.
§ 394. The classes into which the dividend is split up
are called the Membra Dividentia, or Dividing Members.
§ 395. Only two rules need be given for division—
(1) The division must be conducted on a single
basis.
(2) The dividing members must be coextensive with
the divided whole.
OF DIVISION. 117
§ 396. More briefly, we may put the same thing thus —
There must be no cross-division (i) and the division must
be exhaustive (2).
§ 397. The rule, which is commonly given, that each
dividing member must be a common term, is already
provided for under our definition of the process.
§ 398. The rule that the dividend must be predicable
of each of the dividing members is contained in our
second rule ; since, if there were any term of which the
dividend were not predicable, it would be impossible for
the dividing members to be exactly coextensive with it.
It would not do, for instance, to introduce mules and
donkeys into a division of the term horse.
§ 399. Another rule, which is sometimes given, namely,
that the constituent species must exclude one another, is
a consequence of our first; for, if the division be con
ducted on a single principle, the constituent species must
exclude one another. The converse, however, does not
hold true. We may have a division consisting of mutually
exclusive members, which yet involves a mixture of
different bases, e. g. if we were to divide triangle into
scalene, isosceles and equiangular. This happens because
two distinct attributes may be found in invariable con
junction.
§ 400. There is no better test, however, of the sound
ness of a division than to try whether the species overlap,
that is to say, whether there are any individuals that would
fall into two or more of the classes. When this is found
to be the case, we may be sure that wre have mixed two
Il8 OF DIVISION.
or more different fundamenta divisionis. If man, for
instance, were to be divided into European, American,
Aryan, and Semitic, the species would overlap; for both
Europe and America contain inhabitants of Aryan and
Semitic origin. We have here members of a division
based on locality mixed up with members of another
division, which is based on race as indicated by language.
§ 401. The classes which are arrived at by an act of
division may themselves be divided into smaller classes.
This further process is called Subdivision.
§ 402. Let it be noticed that Rule i applies only to a
single act of division. The moment that we begin to
subdivide we not only may, but must, adopt a new basis
of division ; since the old one has, ' ex hypothesi/ been
exhausted. Thus, having divided men according to
the colour of their skins, if we wish to subdivide any of
the classes, we must look out for some fresh attribute
wherein some men of the same complexion differ from
others, e.g. we might divide black men into woolly-haired
blacks, such as the Negroes, and straight-haired blacks,
like the natives of Australia.
§ 403. We will now take an instance of division and
subdivision, with a view to illustrating some of the
technical terms which are used in connection with the
process. Keeping closely to our proper subject, we will
select as an instance a division of the products of thought,
which it is the province of logic to investigate.
OF DIVISION. 1 1 9
Product of thought
Sing
1
Term
I
1
Proposition
Inference
1
I
ular Common
Universal Particular Imn
1
mediate Mediate
A El O
Here we have first a threefold division of the products
of thought based on their comparative complexity. The
first two of these, namely, the term and the proposition,
are then subdivided on the basis of their respective
quantities. In the case of inference the basis of the
division is again the degree of complexity. The sub
division of the proposition is carried a step further than
that of the others. Having exhausted our old basis of
quantity, we take a new attribute, namely, quality, on
which to found the next step of subdivision.
§ 404. Now in such a scheme of division and sub
division as the foregoing, the highest class taken is
known as the Summum Genus. Thus the summum genus
is the same thing as the divided whole, viewed in a
different relation. The term which is called the divided
whole with reference to a single act of division, is called
the summum genus whenever subdivision has taken place.
§ 405. The classes at which the division stops, that is,
any which are not subdivided, are known as the Infimae
Species.
§ 406. All classes intermediate between the summum
genus and the infimae species are called Subaltern Genera
120 OF DIVISION.
or Subaltern Species, according to the way they are
looked at, being genera in relation to the classes below
them and species in relation to the classes above them.
§ 407. Any classes which fall immediately under the
same genus are called Cognate Species, e. g. singular
and common terms are cognate species of term.
§ 408. The classes under which any lower class suc
cessively falls are called Cognate Genera. The relation of
cognate species to one another is like that of children
of the same parents, whereas cognate genera resemble
a line of ancestry.
§ 409. The Specific Difference of anything is the at
tribute or attributes which distinguish it from its cognate
species. Thus the specific difference of a universal pro
position is that the predicate is known to apply to the
whole of the subject. A specific difference is said to
constitute the species.
§ 410. The specific difference of a higher class becomes
a Generic Difference with respect to the class below it.
A generic difference then may be said to be the dis
tinguishing attribute of the whole class to which a given
species belongs. The generic difference is common
to species that are cognate to one another, whereas the
specific difference is peculiar to each. It is the generic
difference of an A proposition that it is universal, the
specific difference that it is affirmative.
§ 411. The same distinction is observed between the
specific and generic properties of a thing. A Specific
Property is an attribute which flows from the difference of
OF DIVISION. I 2 1
a thing itself; a Generic Property is an attribute which
flows from the difference of the genus to which the
thing belongs. It is a specific property of an E proposi
tion that its predicate is distributed, a generic property
that its contrary cannot be true along with it (§ 465) ;
for this last characteristic flows from the nature of the
universal proposition generally.
§ 412. It now remains to say a few words as to the
place in logic of the process of division. Since the
attributes in which members of the same class differ from
one another cannot possibly be indicated by their common
name, they must be sought for by the aid of experience ;
or, to put the same thing in other words, since all the
infimae species are alike contained under the summum
genus, their distinctive attributes can be no more than
separable accidents when viewed in relation to the sum-
mum genus. Hence division, being always founded on
the possession or non-possession of accidental attributes,
seems to lie wholly outside the sphere of formal logic.
This however is not quite the case, for, in virtue of the
Law of Excluded Middle, there is always open to us,
independently of experience, a hypothetical division by
dichotomy. By dichotomy is meant a division into two
classes by a pair of contradictory terms, e.g. a division of
the class, man, into white and not-white. Now we cannot
know, independently of experience, that any members of
the class, man, possess whiteness ; but we may be quite
sure, independently of all experience, that men are either
white or not. Hence division by dichotomy comes strictly
122 OF DIVISION.
within the province of formal logic. Only it must be
noticed that both sides of the division must be hypothetical.
For experience alone can tell us, on the one hand, that
there are any men that are white, and on the other, that
there are any but white men.
§ 413. What we call a division on a single basis is in
reality the compressed result of a scheme of division and
subdivision by dichotomy, in which a fresh principle has
been introduced at every step. Thus when we divide
men, on the basis of colour, into white, black, brown, red
and yellow, we may be held to have first divided men into
white and not-white, and then to have subdivided the
men that are not-white into black and not-black, and
so on. From the strictly formal point of view this division
can only be represented as follows —
Men
White (if any) Not-white (if any)
Black (if any) Not-black (if any)
I !
Brown (if any) Not-brown (if any)
I I
Red (if any) Not-red (if any).
§ 414. Formal correctness requires that the last term in
such a series should be negative. We have here to keep
the term ' not-red ' open, to cover any blue or green men
that might turn up. It is only experience that enables us
to substitute the positive term ' yellow ' for ' not-red,'
OF DIVISION. 123
since we know as a matter of fact that there are no men
but those of the five colours given in the original division.
§ 415. Any correct logical division always admits of
being arrived at by the longer process of division and
subdivision by dichotomy. For instance, the term quad
rilateral, or four-sided rectilinear figure, is correctly divided
into square, oblong, rhombus, rhomboid and trapezium.
The steps of which this division consists are as follows —
Quadrilateral
Parallelogram
Trapezium
I
Rectangle
Non-rectangle
Square Oblong
I |
Rhombus Rhomboid.
§ 416. In reckoning up the infimae species in such
a scheme, we must of course be careful not to include any
class which has been already subdivided ; but no harm
is done by mixing an undivided class, like trapezium, with
the subdivisions of its cognate species.
§ 417. The two processes of definition and division are
intimately connected with one another. Every definition
suggests a division by dichotomy, and every division sup
plies us at once with a complete definition of all its
members.
§ 418. Definition itself, so far as concerns its content,
is, as we have already seen, extraneous to formal logic :
but when once we have elicited a genus and difference out
124 OF DIVISION.
of the material elements of thought, we are enabled, with
out any further appeal to experience, to base thereon
a division by dichotomy. Thus when man has been
defined as a rational animal, we have at once suggested
to us a division of animal into rational and irrational.
§ 419. Again, the addition of the attributes, rational and
irrational respectively, to the common genus, animal, ipso
facto supplies us with definitions of the species, man
and brute. Similarly, when we subdivided rectangle into
square and oblong on the basis of the equality or in
equality of the adjacent sides, we were by so doing
supplied with a definition both of square and oblong —
' A square is a rectangle having all its sides equal/ and
'An oblong is a rectangle which has only its opposite sides
equal.'
§ 420. The definition of a square just given amounts to
the same thing as Euclid's definition, but it complies with
a rule which has value as a matter of method, namely,
that the definition should state the Proximate Genus of the
thing defined.
§ 421. Since definition and division are concerned with
the intension and extension of terms, they are commonly
treated of under the first part of logic : but as the
treatment of the subject implies a familiarity with the
Heads of Predicables, which in their turn imply the pro
position, it seems more desirable to deal with them under
the second.
§ 422. We have already had occasion to distinguish
division from Enumeration. The latter is the statement
OF DIVISION. 125
of the individual things to which a name applies. In
enumeration, as in division, the wider term is predicable of
each of the narrower ones.
§ 423. Partition is the mapping out of a physical
whole into its component parts, as when we say that a
tree consists of roots, stem, and branches. In a partition
the name of the whole is not predicable of each of the
parts.
§ 424. Distinction 'is the separation from one another
of the various meanings of an equivocal term. The term
distinguished is predicable indeed of each of the members,
but of each in a different sense. An equivocal term is
in fact not one but several terms, as would quickly appear,
if we were to use definitions in place of names.
§ 425. We have seen that a logical whole is a genus
viewed in relation to its underlying species. From this
must be distinguished a metaphysical whole, which is a
substance viewed in relation to its attributes, or a class
regarded in the same way. Logically, man is a part of
the class, animal ; metaphysically, animal is contained in
man. Thus a logical whole is a whole in extension,
while a metaphysical whole is a whole in intension. From
the former point of view species is contained in genus ;
from the latter genus is contained in species.
PART III.— OF INFERENCES.
CHAPTER I.
Of Inferences in General.
§ 426. To infer is to arrive at some truth, not by direct
experience, but as a consequence of some truth or truths
already known. If we see a charred circle on the grass,
we infer that somebody has been lighting a fire there,
though we have not seen anyone do it. This conclusion
is arrived at in consequence of our previous experience of
the effects of fire.
§ 427. The term Inference is used both for a process
and for a product of thought.
As a process inference may be defined as the passage
of the mind from one or more propositions to another.
As a product of thought inference may be loosely
declared to be the result of comparing propositions.
§ 428. Every inference consists of two parts —
(1) the truth or truths already known;
(2) the truth which we arrive at therefrom.
The former is called the Antecedent, the latter the Conse
quent. But this use of the terms ' antecedent ' and ' con
sequent ' must be carefully distinguished from the use to
which they were put previously, to denote the two parts of
a complex proposition.
OF INFERENCES IN GENERAL. J2J
§ 429. Strictly speaking, the term inference, as applied
to a product of thought, includes both the antecedent
and consequent : but it is often used for the consequent
to the exclusion of the antecedent. Thus, when we have
stated our premisses, we say quite naturally, ' And the
inference I draw is so and so/
§ 430. Inferences are either Inductive or Deductive.
In induction we proceed from the less to the more
general ; in deduction from the more to the less general,
or, at all events, to a truth of not greater generality than
the one from which we started. In the former we work
up to general principles ; in the latter we work down from
them, and elicit the particulars which they contain.
§ 431. Hence induction is a real process from the
known to the unknown, whereas deduction is no more
than the application of previously existing knowledge ; or,
to put the same thing more technically, in an inductive
inference the consequent is not contained in the ante
cedent, in a deductive inference it is.
§ 432. When, after observing that gold, silver, lead, and
other metals, are capable of being reduced to a liquid
state by the application of heat, the mind leaps to the
conclusion that the same will hold true of some other
metal, as platinum, or of all metals, we have then an in
ductive inference, in which the conclusion, or consequent,
is a new proposition, which was not contained in those
that went before. We are led to this conclusion, not by
reason, but by an instinct which teaches us to expect like
results, under like circumstances. Experience can tell us
128 OF INFERENCES IN GENERAL.
only of the past : but we allow it to affect our notions of
the future through a blind belief that ' the thing that hath
been, it is that which shall be ; and that which is done is
that which shall be done ; and there is no new thing under
the sun.' Take away this conviction, and the bridge is cut
which connects the known with the unknown, the past
with the future. The commonest acts of daily life would
fail to be performed, were it not for this assumption,
which is itself no product of the reason. Thus man's
intellect, like his faculties generally, rests upon a basis of
instinct. He walks by faith, not by sight.
§ 433. It is a mistake to talk of inductive reasoning, as
though it were a distinct species from deductive. The
fact is that inductive inferences are either wholly instinc
tive, and so unsusceptible of logical vindication, or else
they may be exhibited under the form of deductive infer
ences. We cannot be justified in inferring that platinum
will be melted by heat, except where we have equal reason
for asserting the same thing of copper or any other metal.
In fact we are justified in drawing an individual inference
only when we can lay down the universal proposition,
' Every metal can be melted by heat/ But the moment
this universal proposition is stated, the truth of the propo
sition in the individual instance flows from it by way of
deductive inference. Take away the universal, and we
have no logical warrant for arguing from one individual
case to another. We do so, as was said before, only in
virtue of that vague instinct which leads us to anticipate
like results from like appearances.
OF INFERENCES IN GENERAL. 129
§ 434. Inductive inferences are wholly extraneous to the
science of formal logic, which deals only with formal, or
necessary, inferences, that is to say with deductive infer
ences, whether immediate or mediate. These are called
formal, because the truth of the consequent is apparent
from the mere form of the antecedent, whatever be the
nature of the matter, that is, whatever be the terms em
ployed in the proposition or pair of propositions which
constitutes the antecedent. In deductive inference we
never do more than vary the form of the truth from which
we started. When from the proposition ' Brutus was the
founder of the Roman Republic,' we elicit the consequence
' The founder of the Roman Republic was Brutus,' we
certainly have nothing more in the consequent than was
already contained in the antecedent ; yet all deductive in
ferences may be reduced to identities as palpable as this,
the only difference being that in more complicated cases
the consequent is contained in the antecedent along with
a number of other things, whereas in this case the conse
quent is absolutely all that the antecedent contains.
§ 435. On the other hand, it is of the very essence of
induction that there should be a process from the known
to the unknown. Widely different as these two operations
of the mind are, they are yet both included under the
definition which we have given of inference, as the passage
of the mind from one or more propositions to another. It
is necessary to point this out, because some logicians
maintain that all inference must be from the known to the
unknown, whereas others confine it to ' the carrying out
K
130 OF INFERENCES IN GENERAL.
into the last proposition of what was virtually contained in
the antecedent judgements/
§ 436. Another point of difference that has to be noticed
between induction and deduction is that no inductive
inference can ever attain more than a high degree of
probability, whereas a deductive inference is certain, but
its certainty is purely hypothetical.
§ 437. Without touching now on the metaphysical
difficulty as to how we pass at 'all from the known to the
unknown, let us grant that there is no fact better attested
by experience than this—' That where the circumstances
are precisely alike, like results follow.' But then we never
can be absolutely sure that the circumstances in any two
cases are precisely alike. All the experience of all past
ages in favour of the daily rising of the sun is not enough
to render us theoretically certain that the sun will rise to
morrow. We shall act indeed with a perfect reliance upon
the assumption of the coming day-break ; but, for all that,
the time may arrive when the conditions of the universe
shall have changed, and the sun will rise no more.
§ 438. On the other hand a deductive inference has all
the certainty that can be imparted to it by the laws of
thought, or, in other words, by the structure of our mental
faculties ; but this certainty is purely hypothetical. We
may feel assured that if the premisses are true, the conclu
sion is true also. But for the truth of our premisses we
have to fall back upon induction or upon intuition. It is
not the province of deductive logic to discuss the material
truth or falsity of the propositions upon which our reason-
OF INFERENCES IN GENERAL. 13!
ings are based. This task is left to inductive logic, the
aim of which is to establish, if possible, a test of material
truth and falsity.
§ 439. Thus while deduction is concerned only with the
relative truth or falsity of propositions, induction is con
cerned with their actual truth or falsity. For this reason
deductive logic has been termed the logic of consistency,
not of truth.
§ 440. It is not quite accurate to say that in deduction
we proceed from the more to the less general, still less to
say, as is often said, that we proceed from the universal to
the particular. For it may happen that the consequent is
of precisely the same amount of generality as the antece
dent. This is so, not only in most forms of immediate
inference, but also in a syllogism which consists of
singular propositions only, e.g.
The tallest man in Oxford is under eight feet.
So and so is the tallest man in Oxford.
. • . So and so is under eight feet.
This form of inference has been named Traduction ;
but there is no essential difference between its laws and
those of deduction.
§ 441. Subjoined is a classification of inferences, which
will serve as a map of the country we are now about
to explore.
K 2
OF INFERENCES IN GENERAL.
Inference
I
Inductive
Deductive
1
Immediate
1
1
Mediate
1
Simple
Compound
1
Simple
Complex
r : i
1 1 . 1 .
J
.1 , i
Opposi- Conver- Permuta- Conversion Conversion Conjunc- Disjunc- Dilemma,
tion sion tion by by Contra- tive live
Negation position
CHAPTER II.
Of Deductive Inferences.
§ 442. DEDUCTIVE inferences are of two kinds — Immedi
ate and Mediate.
§ 443. An immediate inference is so called because it
is effected without the intervention of a middle term,
which is required in mediate inference.
§ 444. But the distinction between the two might be
conveyed with at least equal aptness in this way — •
An immediate inference is the comparison of two pro
positions directly.
A mediate inference is the comparison of two proposi
tions by means of a third.
§ 445. In that sense of the term inference in which it
is confined to the consequent, it may be said that —
An immediate inference is one derived from a single
O
proposition.
A mediate inference is one derived from two proposi
tions conjointly.
§ 446. There are never more than two propositions in
the antecedent of a deductive inference. Wherever we
134 OF DEDUCTIVE INFERENCES.
have a conclusion following from more than two pro
positions, there will be found to be more than one
inference.
§ 447. There are three simple forms of immediate in
ference, namely Opposition, Conversion and Permutation.
§ 448. Besides these there are certain compound forms,
in which permutation is combined with conversion.
CHAPTER III.
Of Opposition.
§ 449. OPPOSITION is an immediate inference grounded
on the relation between propositions which have the same
terms, but differ in quantity or in quality or in both.
§ 450. In order that there should be any formal opposi
tion between two propositions, it is necessary that their
terms should be the same. There can be no opposition
between two such propositions as these — •
(1) All angels have wings.
(2) No cows are carnivorous.
§ 451. If we are given a pair of terms, say A for subject
and B for predicate, and allowed to affix such quantity
and quality as we please, we can of course make up the
four kinds of proposition recognised by logic, namely,
A. All A is B.
E. No A is B.
I. Some A is B.
O. Some A is not B.
§ 452. Now the problem of opposition is this : Given
the truth or falsity of any one of the four propositions
A, E, I, O, what can be ascertained with regard to the
truth or falsity of the rest, the matter of them being
supposed to be the same ?
OF OPPOSITION.
§ 453. The relations to one another of these four pro
positions are usually exhibited in the following scheme —
A"
. . Contrary . .
E
•
<&'
c/-.
a
g"
\|
E!
5
cf , \
3
3
1
. . Sub-contrary . .
o
§ 454. Contrary Opposition is between two universals
which differ in quality.
§ 455. Sub-contrary Opposition is between two parti
culars which differ in quality.
§ 456. Subaltern Opposition is between two propositions
which differ only in quantity.
§ 457. Contradictory Opposition is between two pro
positions which differ both in quantity and in quality.
§ 458. Subaltern Opposition is also known as Subalter-
nation, and of the two propositions involved the universal
is called the Subalternant and the particular the Subalter-
nate. Both together are called Subalterns, and similarly
in the other forms of opposition the two propositions
involved are known respectively as Contraries, Sub-con
traries and Contradictories.
§ 459. For the sake of convenience some relations are
0
classed under the head of opposition in which there is,
strictly speaking, no opposition at all between the two
propositions involved.
OF OPPOSITION. 137
§ 460. Between sub- contraries there is an apparent, but
not a real opposition, since what is affirmed of one part of
a term may often with truth be denied of another. Thus
there is no incompatibility between the two statements.
(1) Some islands are inhabited.
(2) Some islands are not inhabited.
§ 461. In the case of subaltern opposition the truth
of the universal not only may, but must, be compatible
with that of the particular.
§ 462. Immediate Inference by Relation would be a
more appropriate name than Opposition ; and Relation
might then be subdivided into Compatible and Incom
patible Relation. By ' compatible ' is here meant that
there is no conflict between the truth of the two proposi
tions. Subaltern and sub-contrary opposition would thus
fall under the head of compatible relation ; contrary and
contradictory relation under that of incompatible relation.
Relation
I
Compatible Incompatible
II II
Subaltern Sub-contrary Contrary Contradictory.
§ 463. It should be noticed that the inference in the
case of opposition is from the truth or falsity of one of
the opposed propositions to the truth or falsity of the
other.
§ 464. We will now lay down the accepted laws of
inference with regard to the various kinds of opposition.
138 OF OPPOSITION.
§ 465. Contrary propositions may both be false, but
cannot both be true. Hence if one be true, the other
is false, but not vice versa.
§ 466. Sub-contrary propositions may both be true, but
cannot both be false. Hence if one be false, the other is
true, but not vice versa.
§ 467. In the case of subaltern propositions, if the
universal be true, the particular is true ; and if the particu
lar be false, the universal is false ; but from the truth of
the particular or the falsity of the universal no conclusion
can be drawn.
§ 468. Contradictory propositions cannot be either true
or false together. Hence if one be true, the other is
false, and vice versa.
§ 469. By applying these laws of inference we obtain
the following results —
If A be true, E is false, O false, I true.
If A be false, E is unknown, O true, I unknown.
If E be true, O is true, I falst, A false.
If E be false, O is unknown, I true, A unknown.
If O be true, I is unknown, A false, E unknown.
If O be false, I is true, A true, E false.
If I be true, A is unknown, E false, O unknown.
If I be false, A is false, E true, O true.
§470. It will be seen from the above that we derive
more information from denying a particular than from
denying a universal. Should this seem surprising, the
paradox will immediately disappear, if we reflect that to
deny a universal is merely to assert the contradictory
OF OPPOSITION. 139
particular, whereas to deny a particular is to assert the
contradictory universal. It is no wonder that we should
obtain more information from asserting a universal than
from asserting a particular.
§ 471. We have laid down above the received doctrine
with regard to opposition : but it is necessary to point out
a flaw in it.
When we say that of two sub-contrary propositions,
if one be false, the other is true, we are not taking the
propositions I and O in their now accepted logical
meaning as indefinite (§ 254), but rather in their popular
sense as ' strictly particular ' propositions. For if I
and O were taken as indefinite propositions, meaning
' some, if not all/ the truth of I would not exclude the
possibility of the truth of A, and, similarly, the truth of O
would not exclude the possibility of the truth of E. Now
A and E may both be false. Therefore I and O, being
possibly equivalent to them, may both be false also. In
that case the doctrine of contradiction breaks down as
well. For I and O may, on this showing, be false, without
their contradictories E and A being thereby rendered true.
This illustrates the awkwardness, which we have previously
had occasion to allude to, which ensues from dividing
propositions primarily into universal and particular, instead
of first dividing them into definite and indefinite, and
then subdividing definite propositions into universal and
particular (§ 256).
§ 472. To be suddenly thrown back upon the strictly
particular view of I and O in the special case of opposition,
140 OF OPPOSITION.
after having been accustomed to regard them as indefinite
propositions, is a manifest inconvenience. But the received
doctrine of opposition does not even adhere consistently
to this view. For if I and O be taken as strictly particular
propositions, which exclude the possibility of the universal
of the same quality being true along with them, we ought
not merely to say that I and O may both be true, but that
if one be true the other must also be true. For I being
true, A is false, and therefore O is true ; and we may
argue similarly from the truth of O to the truth of I,
through the falsity of E. Or — to put the same thing in a
less abstract form — since the strictly particular proposition
means ' some, but not all/ it follows that the truth of one
sub-contrary necessarily carries with it the truth of the
other. If we lay down that some islands only are in
habited, it evidently follows, or rather is stated simultane
ously, that there are some islands also which are not
inhabited. For the strictly particular form of proposition
' Some A only is B ' is of the nature of an exclusive proposi
tion, and is really equivalent to two propositions, one affirm
ative and one negative.
§ 473. It is evident from the above considerations that
the doctrine of opposition requires to be amended in one
or other of two ways. Either we must face the conse
quences which follow from regarding I and O as indefinite,
and lay down that sub-contraries may both be false,
accepting the awkward corollary of the collapse of the
doctrine of contradiction ; or we must be consistent with
ourselves in regarding I and O, for the particular purposes
OF OPPOSITION. 141
of opposition, as being strictly particular, and lay down
that it is always possible to argue from the truth of one
sub-contrary to the truth of the other. The latter is un
doubtedly the better course, as the admission of I and O
as indefinite in this connection confuses the theory of
opposition altogether.
§ 474. Of the several forms of opposition contradictory
opposition is logically the strongest. For this three
reasons may be given —
(1) Contradictory opposites differ both in quantity
and in quality, whereas others differ only in
one or the other.
(2) Contradictory opposites are incompatible both as
to truth and falsity, whereas in other cases it is
only the truth or falsity of the two that is in
compatible.
(3) Contradictory opposition is the safest form to
adopt in argument. For the contradictory op
posite refutes the adversary's proposition as
effectually as the contrary, and is not so liable
to a counter-refutation.
§ 475. At first sight indeed contrary opposition appears
stronger, because it gives a more sweeping denial to the
adversary's assertion. If, for instance, some person with
whom we were arguing were to lay down that ' All poets
are bad logicians,' we might be tempted in the heat of
controversy to maintain against him the contrary propo
sition ' No poets are bad logicians/ This would certainly
be a more emphatic contradiction, but, logically con-
142 OF OPPOSITION.
sidered, it would not be as sound a one as the less
obtrusive contradictory, ' Some poets are not bad logi
cians/ which it would be very difficult to refute.
§ 476. The phrase ' diametrically opposed to one
another ' seems to be one of the many expressions which
have crept into common language from the technical
usage of logic. The propositions A and O and E and I
respectively are diametrically opposed to one another in
the sense that the straight lines connecting them constitute
the diagonals of the parallelogram in the scheme of oppo
sition.
§ 477. It must be noticed that in the case of a singular
proposition there is only one mode of contradiction
possible. Since the quantity of such a proposition is at
the minimum, the contrary and contradictory are neces
sarily merged into one. There is no way of denying the
proposition ' This house is haunted/ save by maintaining
the proposition which differs from it only in quality,
namely, ' This house is not haunted.'
§ 478. A kind of generality might indeed be imparted
even to a singular proposition by expressing it in the
form ' A is always B.' Thus we may say, ' This man is
always idle ' — a proposition which admits of being contra
dicted under the form ' This man is sometimes not
idle.'
CHAPTER IV.
Of Conversion.
§ 479. CONVERSION is an immediate inference grounded
on the transposition of the subject and predicate of a^
proposition.
§ 480. In this form of inference the antecedent is tech
nically known as the Convertend, i.e. the proposition to be
converted, and the consequent as the Converse, i.e. the
proposition which has been converted.
§ 481. In a loose sense of the term we may be said to
have converted a proposition when we have merely trans
posed the subject and predicate, when, for instance, we
turn the proposition ' All A is B ' into ' All B is A ' or
1 Some A is not B ' into ' Some B is not A.' But these
propositions plainly do not follow from the former ones,
and it is only with conversion as a form of inference —
with Illative Conversion as it is called — that Logic is
concerned.
§ 482. For conversion as a form of inference two rules
have been laid down —
(1) No term must be distributed in the converse
which was not distributed in the convertend.
(2) The quality of the converse must be the same
as that of the convertend.
144 OF CONVERSION.
§ 483. The first of these rules is founded on the nature
of things. A violation of it involves the fallacy of arguing
from part of a term to the whole.
§ 484. The second rule is merely a conventional one.
We may make a valid inference in defiance of it : but
such an inference will be seen presently to involve some
thing more than mere conversion.
§ 485. There are two kinds of conversion —
(1) Simple.
(2) Per Accidens or by Limitation.
§ 486. We are said to have simply converted a propo
sition when the quantity remains the same as before.
§ 487. We are said to have converted a proposition
per accidens, or by limitation, when the rules for the
distribution of terms necessitate a reduction in the original
quantity of the proposition.
§ 488. A can only be converted per accidens.
E and I can be converted simply.
O cannot be converted at all.
§ 489. The reason why A can only be converted per
accidens is that, being affirmative, its predicate is undis
tributed (§ 293). Since 'All A is B' does not mean
more than ' All A is some B,' its proper converse is ' Some
B is A.' For, if we endeavoured to elicit the inference,
' All B is A,' we should be distributing the term B in the
converse, which was not distributed in the convertend.
Hence we should be involved in the fallacy of arguing
from the part to the whole. Because 'All doctors are
men ' it by no means follows that ' All men are doctors.'
OF CONVERSION. T45
§ 490. E and I admit of simple conversion, because the
quantity of the subject and predicate is alike in each,
both subject and predicate being distributed in E and
undistributed in I.
r No A is B.
J \ . • . No B is A.
( Some A is B.
i . • . Some B is A.
§ 491. The reason why O cannot be converted at all is
that its subject is undistributed and that the proposition is
negative. Now, when the proposition is converted, what
was the subject becomes the predicate, and, as the propo
sition must still be negative, the former subject would now
be distributed, since every negative proposition distributes
its predicate. Hence we should necessarily have a term
distributed in the converse which was not distributed in
the convertend. From ' Some men are not doctors/ it
plainly does not follow that ' Some doctors are not men ' ;
and, generally from ' Some A is not B ' it cannot be in
ferred that ' Some B is not A/ since the proposition
' Some A is not B ' admits of the interpretation that B is
wholly contained in A.
146 OF CONVERSION.
§ 492. It may often happen as a matter of fact that in
some given matter a proposition of the form ' All B is A ' is
true simultaneously with ' All A is B.' Thus it is as true to
say thai? ' All equiangular triangles are equilateral ' as that
' All equilateral triangles are equiangular/ Nevertheless
we are not logically warranted in inferring the one from
the other. Each has to be established on its separate
evidence.
§ 493. On the theory of the quantified predicate the
difference between simple conversion and conversion by
limitation disappears. For the quantity of a proposition
is then no longer determined solely by reference to the
quantity of its subject. ' All A is some B ' is of no
greater quantity than ' Some B is all A/ if both subject
and predicate have an equal claim to be considered.
§ 494. Some propositions occur in ordinary language in
which the quantity of the predicate is determined. This
is especially the case when the subject is a singular term.
Such propositions admit of conversion by a mere trans
position of their subject and predicate, even though they
fall under the form of the A proposition, e. g.
Virtue is the condition of happiness.
. • . The condition of happiness is virtue.
And again,
Virtue is a condition of happiness.
. • . A condition of happiness is virtue.
In the one case the quantity of the predicate is deter
mined by the form of the expression as distributed, in the
other as undistributed.
OF CONVERSION. 147
§ 495. Conversion offers a good illustration of the
principle on which we have before insisted, namely, that
in the ordinary form of proposition the subject is used
in extension and the predicate in intension. For when by
conversion we change the predicate into the subject, we
are often obliged to attach a noun substantive to the
predicate, in order that it may be taken in extension,
instead of, as before, in intension, e.g.
Some mothers are unkind.
. • . Some unkind persons are mothers.
Again,
Virtue is conducive to happiness.
. • . One of the things which are conducive to happi-
ok
ness is virtue.
L 2
CHAPTER V.
Of Permutation.
§ 496. PERMUTATION1 is an immediate inference ground
ed on a change of quality in a proposition and a change of
the predicate into its contradictory- term.
§ 497. In less technical language we may say that per
mutation is expressing negatively what was expressed
affirmatively and vice versa.
§ 498. Permutation is equally applicable to all the four
forms of proposition.
(A) All A is B.
. • . No A is not-B (E).
(E) No A is B.
. • . All A is not-B (A).
(I) Some A is B.
. • . Some A is not not-B (O).
(O) Some A is not B.
. • . Some A is not-B (I).
§ 499. Or, to take concrete examples—
(A) All men are fallible.
. • . No men are not-fallible (E).
(E) No men are perfect.
. • . All men are not-perfect (A).
1 Called by some writers Obversion.
OF PERMUTATION. 149
(I) Some poets are logical.
. • . Some poets are not not-logical (O).
(O) Some islands are not inhabited.
. * . Some islands are not-inhabited (I).
§ 500. The validity of permutation rests on the principle
of excluded middle, namely — That one or other of a pair
of contradictory terms must be applicable to a given
subject, so that, when one may be predicated affirmatively,
the other may be predicated negatively, and vice versa
(§ 31).
§ 501. Merely to alter the qualily of a proposition
would of course affect its meaning ; but when the predi
cate is at the same time changed into its contradictory
term, the original meaning of the proposition is retained,
whilst the form alone is altered. Hence we may lay down
the following practical rule for permutation —
Change the quality of the proposition and change the
predicate into its contradictory term.
§ 502. The law of excluded middle holds only with
regard to contradictories. It is not true of a pair of
positive and privative terms, that one or other of them
must be applicable to any given subject. For the subject
may happen to fall wholly outside the sphere to which
such a pair of terms is limited. But since the fact of
a term being applied is a sufficient indication of its appli
cability, and since within a given sphere positive and
privative terms are as mutually destructive as contra
dictories, we may in all cases substitute the privative for
the negative term in immediate inference by permutation,
150 OF PERMUTATION.
which will bring the inferred proposition more into con
formity with the ordinary usage of language. Thus the
concrete instances given above will appear as follows —
(A) All men are fallible.
. • . No men are infallible (E).
(E) No men are perfect.
. • . All men are imperfect (A).
(I) Some poets are logical.
. • . Some poets are not illogical (O).
(O) Some islands are not inhabited.
. * . Some islands are uninhabited (I).
CHAPTER VI.
Of Compound Forms of Immediate Inference.
§ 503. HAVING now treated of the three simple forms of
immediate inference, we go on to speak of the compound
forms, and first of
Conversion by Negation.
§ 504. When A and O have been permuted, they
become respectively E and I, and, in this form, admit of
simple conversion. We have here two steps of inference :
but the process may be performed at a single stroke, and
is then known as Conversion by Negation. Thus from
' All A is B ' we may infer * No not-B is A/ and again
from ' Some A is not B ' we may infer ' Some not-B is
A.' The nature of these inferences will be seen better in
concrete examples.
§ 505. (A) All poets are imaginative.
. • . No unimaginative persons are poets (E).
(O) Some parsons are not clerical.
. * . Some unclerical persons are parsons (I).
§ 506. The above inferences, when analysed, will be
found to resolve themselves into two steps, namely,
(1) Permutation.
(2) Simple Conversion.
152 OF COMPOUND FORMS
(A) All A is B.
. • . No A is not-B (by permutation).
. • . No not-B is A (by simple conversion).
(0) Some A is not B.
. • . Some A is not-B (by permutation).
. • . Some not-B is A (by simple conversion).
§ 507. The term conversion by negation has been
arbitrarily limited to the exact inferential procedure of
permutation followed by simple conversion. Hence it
necessarily applies only to A and O propositions, since
these when permuted become E and I, which admit of
simple conversion ; whereas E and I themselves are per
muted into A and O, which do not. There seems to be
no good reason, however, why the term ' conversion by
negation ' should be thus restricted in its meaning, instead
of being extended to the combination of permutation with
conversion, no matter in what order the two processes may
be performed. If this is not done, inferences quite as
legitimate as those which pass under the title of conversion
by negation are left without a name.
§ 508. From E and I inferences may be elicited as
follows—
(E) No A is B.
. • . All B is not-A (A).
(1) Some A is B.
. • . Some B is not not-A (O).
(E) No good actions are unbecoming.
. * . All unbecoming actions are not-good (A).
(I) Some poetical persons are logicians.
. • . Some logicians are not unpoetical (O).
OF IMMEDIATE INFERENCE. 153
Or, taking a privative term for our subject,
Some unpractical persons are statesmen.
. * . Some statesmen are not practical.
§ 509. When the inferences just given are analysed, it
will be found that the process of simple conversion pre
cedes that of permutation.
§510. In the case of the E proposition a compound
inference can be drawn even in the original order of the
processes,
No A is B.
. • . Some not-B is A.
No one who employs bribery is honest.
. • . Some dishonest men employ bribery.
The inference here, it must be remembered, does not
refer to matter of fact, but means that one of the possible
forms of dishonesty among men is that of employing
bribery.
§ 511. If we analyse the preceding, we find that the
second step is conversion by limitation.
No A is B.
. • . All A is not-B (by permutation).
. • . Some not-B is A (by conversion per accidens).
§ 512. From A again an inference can be drawn in the
reverse order of conversion per accidens followed by per
mutation —
All A is B.
. • . Some B is not not-A.
All ingenuous persons are agreeable.
. • . Some agreeable persons are not disingenuous.
154 OF COMPOUND FORMS
§ 513. The intermediate link between the above two
propositions is the converse per accidens of the first —
' Some B is A/ This inference, however, coincides with
that from I (§ 508), as the similar inference from E (§ 510)
coincides with that from O (§ 506).
§ 514. All these inferences agree in the essential feature
of combining permutation with conversion, and should
therefore be classed under a common name.
§ 515. Adopting then this slight extension of the term,
we define conversion by negation as — A form of conver
sion in which the converse differs in quality from the con-
vertend, and has the contradictory of one of the original
terms.
§ 516. A still more complex form of immediate infer
ence is known as
Conversion by Contraposition.
This mode of inference assumes the following form —
All A is B.
. • . All not-B is not-A.
All human beings are fallible.
. • . All infallible beings are not-human.
§ 517. This will be found to resolve itself on analysis
into three steps of inference in the following order —
(1) Permutation.
(2) Simple Conversion.
(3) Permutation.
§ 518. Let us verify this statement by performing the
three steps.
OF IMMEDIATE INFERENCE. 155
All A is B.
. • . No A is not-B (by permutation).
. • . No not-B is A (by simple conversion).
. • . All not-B is not-A (by permutation).
All Englishmen are Aryans.
. • . No Englishmen are non-Aryans.
. • . No non-Aryans are Englishmen.
. • . All non- Aryans are non-Englishmen.
§ 519. Conversion by contraposition may be complicated
in appearance by the occurrence of a negative term in the
subject or predicate or both, e.g.
All not-A is B.
. • . All not-B is A.
Again,
All A is not-B.
. • . All B is not-A.
Lastly,
All not-A is not-B.
. • . All B is A.
§ 520. The following practical rule will be found of
use for the right performing of the process —
Transpose the subject and predicate, and substitute
for each its contradictory term.
§ 521. As concrete illustrations of the above forms of
inference we may take the following —
All the men on this board that are not white are
red.
. • . All the men on this board that are not red are
white.
156 OF COMPOUND FORMS
Again,
All compulsory labour is inefficient.
. • . All efficient labour is free (= non-compulsory).
Lastly,
All inexpedient acts are unjust.
. • . All just acts are expedient.
§ 522. Conversion by contraposition may be said to
rest on the following principle —
If one class be wholly contained in another, whatever
is external to the containing class is external also
to the class contained.
§ 523. The same principle may be expressed intensively
as follows —
If an attribute belongs to the whole of a subject,
whatever fails to exhibit that atrribute does not
come under the subject.
§ 524. This statement contemplates conversion by con
traposition only in reference to the A proposition, to which
the process has hitherto been confined. Logicians seem
to have overlooked the fact that conversion by contra
position is as applicable to the O as to the A proposition,
though, when expressed in symbols, it presents a more
clumsy appearance.
OF IMMEDIATE INFERENCE. 157
Some A is not B.
. • . Some not-B is not not-A.
Some wholesome things are not pleasant.
. • . Some unpleasant things are not unwholesome.
§ 525. The above admits of analysis in exactly the
same way as the same process when applied to the A
proposition.
Some A is not B.
. * . Some A is not-B (by permutation).
. • . Some not-B is A (by simple conversion).
. • . Some not-B is not not-A (by permutation).
The result, as in the case of the A proposition, is the
converse by negation of the original proposition per
muted.
§ 526. Contraposition may also be applied to the K
proposition by the use of conversion per accidens in the
place of simple conversion. But, owing to the limitation
of quantity thus effected, the result arrived at is the same
as in the case of the O proposition. Thus from ' No
wholesome things are pleasant ' we could draw the same
inference as before. Here is the process in symbols, when
expanded.
No A is B.
. • . All A is not-B (by permutation).
. • . Some not-B is A (by conversion per accidens).
. • . Some not-B is not not-A (by permutation).
§ 527. In its unanalysed form conversion by contra-
158 OF COMPOUND FORMS
position may be defined generally as — A form of conver
sion in which both subject and predicate are replaced by
their contradictories.
§ 528. Conversion by contraposition differs in several
respects from conversion by negation.
(1) In conversion by negation the converse differs
in quality from the convertend : whereas in
conversion by contraposition the quality of the
two is the same.
(2) In conversion by negation we employ the con
tradictory either of the subject or predicate,
but in conversion by contraposition we employ
the contradictory of both.
(3) Conversion by negation involves only two steps
of immediate inference : conversion by contra
position involves three.
§ 529. Conversion by contraposition cannot be applied
to the ordinary E proposition except by limitation
(§ 526).
From ' No A is B ' we cannot infer ' No not-B is
not-A/ For, if we could, the contradictory of the latter,
namely, ' Some not-B is not-A ' would be false. But it is
manifest that this is not necessarily false. For when one
term is excluded from another, there must be numerous
individuals which fall under neither of them, unless it
should so happen that one of the terms is the direct con
tradictory of the other, which is clearly not conveyed by
the form of the expression ' No A is B/ ' No A is not-A '
stands alone among E propositions in admitting of full
OF IMMEDIATE INFERENCE. 159
conversion by contraposition, and the form of that is the
same after it as before.
§ 530. Nor can conversion by contraposition be applied
at all to I.
From ' Some A is B ' we cannot infer that ' Some not-B
is not-A/ For though the proposition holds true as a
matter of fact, when A and B are in part mutually exclu
sive, yet this is not conveyed by the form of the expression.
It may so happen that B is wholly contained under A,
while A itself contains everything. In this case it will be
true that ' No not-B is not-A,' which contradicts the
attempted inference. Thus from the proposition ' Some
things are substances ' it cannot be inferred that ' Some
not-substances are not-things/ for in this case the contra
dictory is true that ' No not-substances are not-things ' ;
and unless an inference is valid in every case, it is not
formally valid at all.
§ 531. It should be noticed that in the case of the u
proposition immediate inferences are possible by mere
contraposition without conversion.
All A is all B.
. • . All not-A is not-B.
160 OF COMPOUND FORMS, ETC.
For example, if all the equilateral triangles are all the
equiangular, we know at once that all non-equilateral
triangles are also non-equiangular.
§ 532. The principle upon which this last kind of
inference rests is that when two terms are co-extensive,
whatever is excluded from the one is excluded also from
the other.
CHAPTER VII.
Of other Forms of Immediate Inference.
§ 533. HAVING treated of the main forms of immediate
inference, whether simple or compound, we will now
close this subject with a brief allusion to some other forms
which have been recognised by logicians.
§ 534. Every statement of a relation may furnish us
with an immediate inference in which the same fact is
presented from the opposite side. Thus from ' John hit
James ' we infer ' James was hit by John ' ; from ' Dick is
the grandson of Tom ' we infer ' Tom is the grandfather
of Dick ' ; from ' Bicester is north-east of Oxford ' we
infer ' Oxford is south-west of Bicester ' ; from ' So and so
visited the Academy the day after he arrived in London '
we infer ' So and so arrived in London the day before he
visited the Academy ' ; from * A is greater than B ' we
infer ' B is less than A ' ; and so on without limit. Such
inferences as these are material, not formal. No law can
be laid down for them except the universal postulate,
that
' Whatever is true in one form of words is true in
every other form of words which conveys the
same meaning.'
1 62 OF OTFIER FORMS
§ 535. There is a sort of inference which goes under
the title of Immediate Inference by Added Determinants,
in which from some proposition already made another is
inferred, in which the same attribute is attached both to
the subject and the predicate, e.g.
A horse is a quadruped.
. • . A white horse is a white quadruped.
§ 536. Such inferences are very deceptive. The attri
butes added must be definite qualities, like whiteness, and
must in no way involve a comparison. From ' A horse is
a quadruped ' it may seem at first sight to follow that
4 A swift horse is a swift quadruped.' But we need not
go far to discover how little formal validity there is about
such an inference. From ' A horse is a quadruped ' it by
no means follows that * A slow horse is a slow quadruped ' ;
for even a slow horse is swift compared with most quad
rupeds. All that really follows here is that ' A slow horse
is a quadruped which is slow for a horse/ Similarly,
from ' A Bushman is a man ' it does not follow that ' A
tall Bushman is a tall man,' but only that ' A tall Bush
man is a man who is tall for a Bushman'; and so on
generally.
§ 537. Very similar to the preceding is the process known
as Immediate Inference by Complex Conception, e.g.
A horse is a quadruped.
. • . The head of a horse is the head of a quadruped.
§ 538. This inference, like that by added determinants,
from which it differs in name rather than in nature, may
be explained on the principle of Substitution. Starting
OF IMMEDIATE INFERENCE. 163
from the identical proposition, * The head of a quadruped
is the head of a quadruped,' and being given that 'A
horse is a quadruped/ so that whatever is true of ' quad
ruped ' generally we know to be true of ' horse/ we are
entitled to substitute the narrower for the wider term, and
in this manner we arrive at the proposition,
The head of a horse is the head of a quadruped.
§ 539. Such an inference is valid enough, if the same
caution be observed as in the case of added determinants,
that is, if no difference be allowed to intervene in the rela
tion of the fresh conception to the generic and the specific
terms.
M 2
CHAPTER VIII.
Of Mediate Inferences or Syllogisms.
§ 540. A MEDIATE Inference, or Syllogism, consists of
two propositions, which are called the Premisses, and a
third proposition known as the Conclusion, which flows
from the two conjointly.
§ 541. In every syllogism two terms are compared with
one another by means of a third, which is called the
Middle Term. In the premisses each of the two terms
is compared separately with the middle term ; and in the
conclusion they are compared with one another.
§ 542. Hence every syllogism consists of three terms,
one of which occurs twice in the premisses and does not
appear at all in the conclusion. This term is called the
Middle Term. The predicate of the conclusion is called
the Major Term and its subject the Minor Term.
§ 543. The major and minor terms are called the
Extremes, as opposed to the Mean or Middle Term.
§ 544. The premiss in which the major term is com
pared with the middle is called the Major Premiss.
§ 545. The other premiss, in which the minor term is
compared with the middle, is called the Minor Premiss.
§ 546. The order in which the premisses occur in a
OF MEDIATE INFERENCES OR SYLLOGISMS. 165
syllogism is indifferent, but it is usual, for convenience, to
place the major premiss first.
§ 547. The following will serve as a typical instance of
a syllogism —
Middle term Major term \
Major Premiss. All mammals are warm-blooded I Antecedent
Minor term Middle term (
Minor Premiss. All whales are mammals
Minor term Major term \ Consequent or
. • . All whales are warm-blooded j Conclusion.
§ 548. The reason why the names ' major/ ' middle '
and ' minor ' terms were originally employed is that in
an affirmative syllogism such as the above, which was
regarded as the perfect type of syllogism, these names
express the relative quantity in extension of the three
terms.
§ 549. It must be noticed however that, though the
middle term cannot be of larger extent than the major
nor of smaller extent than the minor, if the latter be
distributed, there is nothing to prevent all three, or any
two of them, from being coextensive.
§ 550. Further, when the minor term is undistributed,
we either have a case of the intersection of two classes,
from which it cannot be told which of them is the larger,
i66
OF MEDIATE INFERENCES
or the minor term is actually larger than the middle, when
it stands to it in the relation of genus to species, as in the
following syllogism —
All Negroes have woolly hair.
Some Africans are Negroes.
. • . Some Africans have woolly hair.
§ 551. Hence the names are not applied with strict
accuracy even in the case of the affirmative syllogism ;
and when the syllogism is negative, they are not appli
cable at all : since in negative propositions we have no
means of comparing the relative extension of the terms
employed. Had we said in the major premiss of our
typical syllogism, ' No mammals are cold-blooded/ and
drawn the conclusion ' No whales are cold-blooded/ we
could not have compared the relative extent of the terms
' mammal ' and ' cold-blooded/ since one has been simply
excluded from the other.
§ 552. So far we have rather described than defined the
OR SYLLOGISMS. 167
syllogism. All the products of thought, it will be remem
bered, are the results of comparison. The syllogism,
which is one of them, may be so regarded in two
ways —
(1) As the comparison of two propositions by means
of a third.
(2) As the comparison of two terms by means of
a third or middle term.
§ 553. The two propositions which are compared with
one another are the major premiss and the conclusion,
which are brought into connection by means of the minor
premiss. Thus in the syllogism above given we compare
the conclusion 'All whales are warm-blooded' with the
major premiss " All mammals are warm-blooded,' and
find that the former is contained "under the latter, as soon
as we become acquainted with the intermediate proposi
tion ' All whales are mammals.'
§ 554. The two terms which are compared with one
another are of course the major and minor.
§ 555. The syllogism is merely a form into which our
deductive inferences may be thrown for the sake of ex
hibiting their conclusiveness. It is not the form which
they naturally assume in speech or writing. Practically
the conclusion is generally stated first and the premisses
introduced by some causative particle as 'because,' 'since,'
'for,' &c. We start with our conclusion, and then give
the reason for it by supplying the premisses.
§ 556. The conclusion, as thus stated first, was called
by logicians the Problema or Quaestio, being regarded as
1 68 OF MEDIATE INFERENCES OR SYLLOGISMS.
a problem or question, to which a solution or answer was
to be found by supplying the premisses.
§ 557. In common discourse and writing the syllogism
is usually stated defectively, one of the premisses or, in
some cases, the conclusion itself being omitted. Thus
instead of arguing at full length
All men are fallible,
The Pope is a man,
. • . The Pope is fallible,
we content ourselves with saying ' The Pope is fallible, for
he is a man,' or ' The Pope is fallible, because all men
are so ' ; or perhaps we should merely say ' All men are
fallible, and the Pope is a man,' leaving it to the sagacity
of our hearers to supply the desired conclusion. A
syllogism, as thus elliptically stated, is commonly, though
incorrectly, called an Enthymeme. When the major
premiss is omitted, it is called an Enthymeme of the First
Order; when the minor is omitted, an Enthymeme of the
Second Order ; and when the conclusion is omitted an
Enthymeme of the Third Order.
CHAPTER IX.
Of Mood and Figure.
§ 558. SYLLOGISMS may differ in two ways —
(1) in Mood ;
(2) in Figure.
§ 559. Mood depends upon the kind of propositions
employed. Thus a syllogism consisting of three universal
affirmatives, AAA, would be said to differ in mood from
one consisting of such propositions as EIO or any other
combination that might be made. The syllogism pre
viously given to prove the fallibility of the Pope belongs
to the mood AAA. Had we drawn only a particular
conclusion, ' Some Popes are fallible/ it would have fallen
into the mood AAI.
§ 560. Figure depends upon the arrangement of the
terms in the propositions. Thus a difference of figure is
internal to a difference of mood, that is to say, the same
mood can be in any figure.
§ 561. We will now show how many possible varieties
there are of mood and figure, irrespective of their logical
validity.
§ 562. And first as to mood.
Since every syllogism consists of three propositions,
and each of these propositions may be either A, E, I, or
O, it is clear that there will be as many possible moods as
170 OF MOOD AND FIGURE.
there can be combinations of four things, taken three
together, with no restrictions as to repetition. It will be
seen that there are just sixty-four of such combinations.
For A may be followed either by itself or by E, I, or O.
Let us suppose it to be followed by itself. Then this pair
of premisses, AA, may have for its conclusion either
A, E, I, or O, thus giving four combinations which com
mence with AA. In like manner there will be four
commencing with AE, four with AI, and four with
AO, giving a total of sixteen combinations which com
mence with A. Similarly there will be sixteen com
mencing with E, sixteen with I, sixteen with O — in all
sixty-four. It is very few, however, of these possible
combinations that will be found legitimate, when tested by
the rules of syllogism.
§ 563. Next as to figure.
There are four possible varieties of figure in a syllogism,
as may be seen by considering the positions that can be
occupied by the middle term in the premisses. For as
there are only two terms in each premiss, the position
occupied by the middle term necessarily determines that
of the others. It is clear that the middle term must either
occupy the same position in both premisses or not, that is,
it must either be subject in both or predicate in both, or
else subject in one and predicate in the other. Now, if
we are not acquainted with the conclusion of our syllogism,
we do not know which is the major and which the minor
term, and have therefore no means of distinguishing
between one premiss and another ; consequently we
OF MOOD AND FIGURE. 171
must stop here, and say that there are only three different
arrangements possible. But, if the conclusion also be
assumed as known, then we are able to distinguish one
premiss as the major and the other as the minor ; and so
we can go further, and lay down that, if the middle term
does not hold the same position in both premisses, it must
either be subject in the major and predicate in the
minor, or else predicate in the major and subject in the
minor.
§ 564. Hence there result
The Four Figures.
When the middle term is subject in the major and
predicate in the minor, we are said to have the First
Figure.
When the middle term is predicate in both premisses,
we are said to have the Second Figure.
When the middle term is subject in both premisses, we
are said to have the Third Figure.-
When the middle term is predicate in the major premiss
and subject in the minor, we are said to have the Fourth
Figure.
§ 565. Let A be the major term ;
B the middle.
C the minor.
Figure I.
Figure II.
Figure III.
Figure IV.
B— A
A— B
B— A
A— B
C— B
C— B
B— C
B— C
C— A
C— A
C— A
C— A
1/2 OF MOOD AND FIGURE.
All these figures are legitimate, though the fourth is
comparatively valueless.
§ 566. It will be well to explain by an instance the
meaning of the assertion previously made, that a difference
of figure is internal to a difference of mood. We will
take the mood EIO, and by varying the position of the
terms, construct a syllogism in it in each of the four
figures.
E No wicked man is happy.
I Some prosperous men are wicked.
0 . • . Some prosperous men are not happy.
II.
E No happy man is wicked.
1 Some prosperous men are wicked.
0 . • . Some prosperous men are not happy.
III.
E No wicked man is happy.
1 Some wicked men are prosperous.
0 . • . Some prosperous men are not happy.
IV.
E No happy man is wicked.
1 Some wicked men are prosperous.
O . • . Some prosperous men are not happy.
§ 567. In the mood we have selected, owing to the
peculiar nature of the premisses, both of which admit of
OF MOOD AND FIGURE. 173
simple conversion, it happens that the resulting syllogisms
are all valid. But in the great majority of moods no
syllogism would be valid at all, and in many moods a
syllogism would be valid in one figure and invalid in
another. As yet however we are only concerned with the
conceivable combinations, apart from the question of their
legitimacy.
§ 568. Now since there are four different figures and
sixty-four different moods, we obtain in all 256 possible
ways of arranging three terms in three propositions, that
is, 256 possible forms of syllogism.
CHAPTER X.
Of the Canon of Reasoning.
§ 569. THE first figure was regarded by logicians as the
only perfect type of syllogism, because the validity of moods
in this figure may be tested directly by their complying, or
failing to comply, with a certain axiom, the truth of which
is self-evident. This axiom is known as the Dictum de
Omni et Nullo. It may be expressed as follows —
Whatever may be affirmed or denied of a whole class
may be affirmed or denied of everything contained in that
class.
§ 570. This mode of stating the axiom contemplates
predication as being made in extension, whereas it is more
naturally to be regarded as being made in intension.
§ 571. The same principle maybe expressed intensively
as follows —
Whatever has certain attributes has also the attributes
which invariably accompany them l.
1 Nota notae est nota rei ipsius. ' Whatever has any mark has
that which it is a mark of.' Mill, vol. i, p. 201.
OF THE CANON OF REASONING. 175
§ 572. By Aristotle himself the principle was expressed
in a neutral form thus —
' Whatever is stated of the predicate will be stated also
of the subject V
This way of putting it, however, is too loose.
§ 573. The principle precisely stated is as follows —
Whatever may be affirmed or denied universally of the
predicate of an affirmative proposition, may be affirmed or
denied also of the subject.
§ 574. Thus, given an affirmative proposition ' Whales
are mammals/ if we can affirm anything universally of
the predicate ' mammals/ as, for instance, that ' All
mammals are warm-blooded/ we shall be able to affirm
the same of the subject ' whales ' ; and, if we can deny
anything universally of the predicate, as that ' No mammals
are oviparous/ we shall be able to deny the same of the
subject.
§ 575. In whatever way the supposed canon of reason
ing may be stated, it has the defect of applying only to a
single figure, namely, the first. The characteristic of the
reasoning in that figure is that some general rule is main
tained to hold good in a particular case. The major pre
miss lays down some general principle, whether affirma
tive or negative ; the minor premiss asserts that a particular
case falls under this principle ; and the conclusion applies
the general principle to the particular case. But though
all syllogistic reasoning may be tortured into conformity
1 "Qaa Kara rov KaTrjyopov/j.(vov \fyerai, iravra /mi Kara TOV VTTO-
i. Cat. 3, § I.
176 OF THE CANON OF REASONING.
with this type, some of it finds expression more naturally
in other ways.
§ 576. Modern logicians therefore prefer to abandon
the Dictum de Omni et Nullo in any shape, and to sub
stitute for it the following three axioms, winch apply to all
figures alike.
Three Axioms of Mediate Inference.
(1) If two terms agree with the same third term, they
agree with one another.
(2) If one term agrees, and another disagrees.
with the same third term, they disagree with
one another.
(3) If two terms disagree with the same third term,
they may or may not agree with one an
other.
§ 577. The first of these axioms is the principle of all
affirmative, the second of all negative, syllogisms ; the third
points out the conditions under which no conclusion can
be drawn. If there is any agreement at all between the
two terms and the third, as in the cases contemplated in
the first and second axioms, then we have a conclusion of
some kind : if it is otherwise, we have none.
§ 578. It must be understood with regard to these
axioms that, when we speak of terms agreeing or dis
agreeing with the same third term, we mean that they
agree or disagree with the same part of it.
§ 579. Hence in applying these axioms it is necessary
OF THE CANON OF REASONING. 177
to bear in mind the rules for the distinction of terms.
Thus from M fi .g A
No C is B,
the only inference which can be drawn is that Some
A is not C (which alters the figure from the first to the
fourth). For it was only part of A which was known to
agree with B. On the theory of the quantified predicate
we could draw the inference No C is some A.
§ 580. It is of course possible for terms to agree with
different parts of the same third term, and yet to have no
connection with one another. Thus
All birds fly.
All bats fly.
But we do not infer therefrom that bats are birds or vice
versa\
§ 581. On the other hand, had we said,—
All birds lay eggs,
No bats lay eggs,
we might confidently have drawn the conclusion
No bats are birds.
For the term ' bats/ being excluded from the whole of the
term ' lay eggs/ is thereby necessarily excluded from that
part of it which coincides with ' birds,'
CHAPTER XL
Of the General Rules of Syllogism.
§ 582. WE now proceed to lay down certain general
rules to which all valid syllogisms must conform. These
are divided into primary and derivative.
I. Primary.
(1) A syllogism must consist of three propositions
only.
(2) A syllogism must consist of three terms only.
(3) The middle term must be distributed at least
once in the premisses.
(4) No term must be distributed in the conclusion
which was not distributed in the premisses.
(5) Two negative premisses prove nothing.
(6) If one premiss be negative, the conclusion must
be negative.
(7) If the conclusion be negative, one of the pre
misses must be negative : but if the conclusion
be affirmative, both premisses must be affirma
tive.
II. Derivative.
(8) Two particular premisses prove nothing.
(9) If one premiss be particular, the conclusion must
be particular.
OF THE GENERAL RULES OF SYLLOGISM. 179
§ 583. The first two of these rules are involved in the
definition of the syllogism with which we started. We
said it might be regarded either as the comparison of two
propositions by means of a third or as the comparison of
two terms by means of a third. To violate either of these
rules therefore would be inconsistent with the fundamental
conception of the syllogism. The first of our two defini
tions indeed (§ 552) applies directly only to syllogisms in
the first figure ; but since all syllogisms may be ex
pressed, as we shall presently see, in the first figure, it
applies indirectly to all. When any process of mediate
inference appears to have more than two premisses, it will
always be found that there is more than one syllogism.
If there are less than three propositions, as in the
fallacy of c begging the question/ in which the conclusion
simply reiterates one of the premisses, there is no syllogism
at all.
With regard to the second rule, it is plain that any
attempted syllogism which has more than three terms
cannot conform to the conditions of any of the axioms of
mediate inference.
§ 584. The next two rules guard against the two
fallacies which are fatal to most syllogisms whose con
stitution is unsound.
§ 585. The violation of Rule 3 is known as the Fallacy
of Undistributed Middle. The reason for this rule is not
far to seek. For if the middle term be not used in either
premiss in its whole extent, we may be referring to one
part of it in one premiss and to quite another part of it in
N 2
j8o OF THE GENERAL
another, so that there will be really no middle term at all.
From such premisses as these —
All pigs are omnivorous,
All men are omnivorous,
it is plain that nothing follows. Or again, take these
premisses —
Some men are fallible,
All Popes are men.
Here it is possible that ' All Popes ' may agree with pre
cisely that part of the term ( man,' of which it is not known
whether it agrees with * fallible ' or not.
§ 586. The violation of Rule 4 is known as the Fallacy
of Illicit Process. If the major term is distributed in the
conclusion, not having been distributed in the premiss, we
have what is called Illicit Process of the Major; if the
same is the case with the minor term, we have Illicit
Process of the Minor.
§ 587. The reason for this rule is that if a term be used
in its whole extent in the conclusion, which was not so
used in the premiss in which it occurred, we would be
arguing from the part to the whole. It is the same sort
of fallacy which we found to underlie the simple conversion
of an A proposition.
§ 588. Take for instance the following —
All learned men go mad.
John is not a learned man.
. • . John will not go mad.
In the conclusion 'John' is excluded from the whole
class of persons who go mad, whereas in the premisses,
RULES OF SYLLOGISM. l8l
granting that all learned men go mad, it has not been said
that they are all the men who do so. We have here an
illicit process of the major term.
§ 589. Or again take the following —
All Radicals are covetous.
All Radicals are poor.
. • . All poor men are covetous.
The conclusion here is certainly not warranted by our
premisses. For in them we spoke only of some poor men,
since the predicate of an affirmative proposition is undis
tributed.
§ 590. Rule 5 is simply another way of stating the third
axiom of mediate inference. To know that two terms
disagree with the same third term gives us no ground for
any inference as to whether they agree or disagree with
one another, e.g.
Ruminants are not oviparous.
Sheep are not oviparous.
For ought that can be inferred from the premisses, sheep
may or may not be ruminants.
§ 591. This rule may sometimes be violated in appear
ance, though not in reality. For instance, the following
is perfectly legitimate reasoning.
No remedy for corruption is effectual that does not
render ituseless.
Nothing but the ballot renders corruption useless.
. • . Nothing but the ballot is an effectual remedy for
corruption.
1 82 OF THE GENERAL
But on looking into this we find that there are four
terms — •
No not-A is B.
No not-C is A.
. • . No not-C is B.
The violation of Rule 5 is here rendered possible by
the additional violation of Rule 2. In order to have the
middle term the same in both premisses we are obliged to
make the minor affirmative, thus
No not-A is B.
All not-C is not-A.
. • . No not-C is B.
No remedy that fails to render corruption useless* is
effectual.
All but the ballot fails to render corruption useless.
. • . Nothing but the ballot is effectual.
§ 592. Rule 6 declares that, if one premiss be negative,
the conclusion must be negative. Now in compliance
with Rule 5, if one premiss be negative, the other must
be affirmative. We have therefore the case contemplated
in the second axiom, namely, of one term agreeing and
the other disagreeing with the same third term ; and we
know that this can only give ground for a judgement of
disagreement between the two terms themselves — in other
words, to a negative conclusion.
§ 593. Rule 7 declares that, if the conclusion be nega
tive, one of the premisses must be negative : but, if the
RULES OF SYLLOGISM. 183
conclusion be affirmative, both premisses must be affirma
tive. It is plain from the axioms that a judgement of
disagreement can only be elicited from a judgement of
agreement combined with a judgement of disagreement,
and that a judgement of agreement can result only from
two prior judgements of agreement.
§ 594. The seven rules already treated of are evident
by their own light, being of the nature of definitions and
axioms : but the two remaining rules, which deal with
particular premisses, admit of being proved from their
predecessors.
§ 595. Proof of Rule 8. — That two particular premisses
prove nothing.
We know by Rule 5 that both premisses cannot be
negative. Hence they must be either both affirmative, II,
or one affirmative and one negative, IO or OI.
Now II premisses do not distribute any term at all, and
therefore the middle term cannot be distributed, which
would violate Rule 3.
Again in IO or OI premisses there is only one term
distributed, namely, the predicate of the O proposition.
But Rule 3 requires that this one term should be the
middle term. Therefore the major term must be undis
tributed in the major premiss. But since one of the
premisses is negative, the conclusion must be negative, by
Rule 6. And every negative proposition distributes its
predicate. Therefore the major term must be distributed
where it occurs as predicate of the conclusion. But it was
not distributed in the major premiss. Therefore in
1 84 OF THE GENERAL
drawing any conclusion we violate Rule 4 by an illicit
process of ihe major term.
§ 596. Proof of Rule 9. — That^ if one premiss be par
ticular, the conclusion must be particular.
Two negative premisses being excluded by Rule 5, and
two particular by Rule 8, the only pairs of premisses we
can have are —
AI, AO, EL
Of course the particular premiss may precede the
universal, but the order of the premisses will not affect
the reasoning.
AI premisses between them distribute one term only.
This must be the middle term by Rule 3. Therefore the
conclusion must be particular, as its subject cannot be
distributed.
AO and El premisses each distribute two terms, one
of which must be the middle term by Rule 3 : so that
there is only one term left which may be distributed in the
conclusion. But the conclusion must be negative by
Rule 4. Therefore its predicate must be distributed.
Hence its subject cannot be so. Therefore the con
clusion must be particular.
§ 597. Rules 6 and 9 are often lumped together in a
single expression — ' The conclusion must follow the
weaker part/ negative being considered weaker than
affirmative, and particular than universal.
§ 598. The most important rules of syllogism are
summed up in the following mnemonic lines, which
appear to have been perfected, though not invented, by
RULES OF SYLLOGISM. 185
a mediaeval logician known as Petrus Hispanus, who was
afterwards raised to the Papal Chair under the title of
Pope John XXI, and who died in 1277 —
Distribuas medium, nee quartus terminus adsit;
Utraque nee praemissa negans, nee particularis ;
Sectetur partem conclusio deteriorem,
Et non distribuat, nisi cum praemissa, negetve.
CHAPTER XII.
Of the Determination of the Legitimate Moods
of Syllogism.
§ 599. IT will be remembered that there were found to
be 64 possible moods, each of which might occur in any
of the four figures, giving us altogether 256 possible
varieties of syllogism. The task now before us is to
determine how many of these combinations of mood and
figure are legitimate.
§ 600. By the application of the preceding rules we are
enabled to reduce the 64 possible moods to 1 1 valid ones.
This may be done by a longer or a shorter method. The
longer method, which is perhaps easier of comprehension,
is to write down the 64 possible moods, and then strike
out such as violate any of the rules of syllogism.
AAA AEA- AIA AOA
AA^ AEE AH± AQE-
AAI -AEI- All AQ£
-AAO- AEO AIO AGO
EIO
LEGITIMATE MOODS OF SYLLOGISM. 187
4AA- 4EA-
IAI 4EJ-
T A O TF.O
~A / i. v_/ ~z XtrXl/"
-QAA
OAF
Tl7iT±:7~
-0AI- Qfil
OAO 0EQ 0IQ 0O(
§ 601. The batches which are crossed are those in
which the premisses can yield no conclusion at all, owing
to their violating Rule 6 or 9; in the rest the premisses are
legitimate, but a wrong conclusion is drawn from each of
them as are translineated.
§ 602. IEO stands alone, as violating Rule 4. 't his
may require a little explanation.
Since the conclusion is negative, the major term, which
is its predicate, must be distributed. But the major
premiss, being I, does not distribute either subject or
predicate. Hence IEO must always involve an illicit
process of the major.
§ 603. The 1 1 moods which have been left valid, after
being tested by the syllogistic rules, are as follows —
AAA. AAI. AEE. AEO. AIL AOO.
EAE. EAO. EIO.
IAI.
OAO.
§ 604. We will now arrive at the same result by a
shorter and more scientific method. This method consists
1 88 LEGITIMATE MOODS OF SYLLOGISM.
in first determining what pairs of premisses are valid in
accordance with Rules 6 and 9, and then examining what
conclusions may be legitimately inferred from them in
accordance with the other rules of syllogism.
§ 605. The major premiss may be either A, E, I or O.
If it is A, the minor also may be either A, E, I or O. If
it is E, the minor can only be A or I. If it is I, the minor
can only be A or E. If it is O, the minor can only be A.
Hence there result 9 valid pairs of premisses.
AA. AE. AI. AO.
EA. EL
IA. IE.
OA.
Three of these pairs, namely AA, AE, EA, yield two
conclusions apiece, one universal and one particular, which
do not violate any of the rules of syllogism ; one of them,
IE, yields no conclusion at all ; the remaining five have
their conclusion limited to a single proposition, on the
principle that the conclusion must follow the weaker part.
Hence we arrive at the same result as before, of 1 1 legiti
mate moods —
AAA. AAI. AEE. AEO. EAE. EAO.
All. AGO. EIO. IAL OAO.
CHAPTER XIII.
Of the Special Rides of the Four Figures.
§ 606. OUR next task must be to determine how far the
1 1 moods which we arrived at in the last chapter are valid
in the four figures. But before this can be done, we must
lay down the
Special Rules of the Four Figures.
FIGURE I.
Rule i. The minor premiss must be affirmative.
Rule 2. The major premiss must be universal.
FIGURE II.
Rule i. One or other premiss must be negative.
Rule 2. The conclusion must be negative.
Rule 3. The major premiss must be universal.
FIGURE III.
Rule i. The minor premiss must be affirmative.
Rule 2. The conclusion must be particular.
FIGURE IV.
Rule i. When the major premiss is affirmative, the
minor must be universal.
Rule 2. When the minor premiss is particular, the
major must be negative.
1 90 OF THE SPECIAL RULES
Rule 3. When the minor premiss is affirmative, the
conclusion must be particular.
Rule 4. When the conclusion is negative, the
major premiss must be universal.
Rule 5. The conclusion cannot be a universal
affirmative.
Rule 6. Neither of the premisses can be a parti
cular negative.
§ 607. The special rules of the first figure are merely
a reassertion in another form of the Dictum de Omni et
Nullo. For if the major premiss were particular, -we
should not have anything affirmed or denied of a whole
class ; and if the minor premiss were negative, wre should
not have anything declared to be contained in that class.
Nevertheless these rules, like the rest, admit of being
proved from the position of the terms in the figure,
combined with the rules for the distribution of terms
(§ 293).
Proof of the Special Rules of the Four Figures.
FIGURE I.
§ 608. Proof of Rule i. — The minor premiss must be
affirmative. B — A
If possible, let the minor premiss be negative. C — B
Then the major must be affirmative (by Rule 5 1), C — A
and the conclusion must be negative (by Rule 6). But
the major being affirmative, its predicate is undistributed ;
and the conclusion being negative, its predicate is dis-
1 This refers to the General Rules of Syllogism.
OF THE FOUR FIGURES. 191
tributed. Now the major term is in this figure predicate
both in the major premiss and in the conclusion. Hence
there results illicit process of the major term. Therefore
the minor premiss must be affirmative.
§ 609. Proof of Rule 2. — The major premiss must be
universal.
Since the minor premiss is affirmative, the middle term,
-which is its predicate, is undistributed there. Therefore
it must be distributed in the major premiss, where it is
subject. Therefore the major premiss must be universal.
FIGURE II.
§610. Proof of Rule i. — One or other premiss must be
negative.
The middle term being predicate in both A — B
premisses, one or other must be negative ; else C — B
there would be undistributed middle. C — A
§611. Proof of Rule 2. — The conclusion must be negative.
Since one of the premisses is negative, it follows that
the conclusion also must be so (by Rule 6).
§ 612. Proof of Rule 3. — The major premiss must be
universal.
The conclusion being negative, the major term will
there be distributed. But the major term is subject in
the major premiss. Therefore the major premiss must
be universal (by Rule 4).
FIGURE III.
§ 613. Proof of Rule i. — The minor premiss must be
affirmative.
192 OF THE SPECIAL RULES
The proof of this rule is the same as in the B — A
first figure, the two figures being alike so far as B - — C
the major term is concerned. C — A
§ 614. Proof of Rule 2. — The conclusion must be par
ticular.
The minor premiss being affirmative, the minor term,
which is its predicate, will be undistributed there. Hence
it must be undistributed in the conclusion (by Rule 4).
Therefore the conclusion must be particular.
FIGURE IV.
§ 615. Proof of Rule i. — When the major premiss is
affirmative, the minor must be universal*
If the minor were particular, there would be undistri
buted middle J.
§ 616. Proof of Rule 2. — When the minor A — B
premiss is particular, the major must be negative. B — C
This rule is the converse of the preceding, C — A
and depends upon the same principle.
§617. Proof of Rule 3. — When the minor premiss is
affirmative, the conclusion must be particular.
If the conclusion were universal, there would be illicit
process of the minor.
§ 618. Proof of Rule 4. — When the conclusion is negative,
the major premiss must be universal.
If the major premiss were particular, there would be
illicit process of the major.
1 Shorter proofs are employed in this figure, as the student is by
this time familiar with the method of procedure.
OF THE FOUR FIGURES. 193
§619. Proof of Rule 5. — The conclusion cannot be a
universal affirmative.
The conclusion being affirmative, the premisses must be
so too (by Rule 7). Therefore the minor term is undistri
buted in the minor premiss, where it is predicate. Hence
it cannot be distributed in the conclusion (by Rule 4).
Therefore the affirmative conclusion must be particular.
§ 620. Proof of Rule 6.— Neither of the premisses can
be a particular negative.
If the major premiss were a particular negative, the
conclusion would be negative. Therefore the major term
would be distributed in the conclusion. But the major
premiss being particular, the major term could not be
distributed there. Therefore we should have an illicit
process of the major term.
If the minor premiss were a particular negative, then,
since the major must be affirmative (by Rule 5), we should
have undistributed middle.
CHAPTER XIV.
Of the Determination of the Moods that are
valid in the Four Figiires.
§ 621. BY applying the special rules just given we shall
be able to determine how many of the eleven legitimate
moods are valid in the four figures.
§ 622. These eleven legitimate moods were found to be
AAA. AAI. AEE. AEO. All. AGO. EAE.
EAO. EIO. IAI. OAO.
FIGURE I.
§ 623. The rule that the major premiss must be uni
versal excludes the last two moods, IAI, OAO. The rule
that the minor premiss must be affirmative excludes three
more, namely, AEE, AEO, AOO.
Thus we are left with six moods which are valid in the
first figure, namely,
AAA. EAE. AIL EIO. AAI. EAO.
FIGURE II.
§ 624. The rule that one premiss must be negative
excludes four moods, namely, AAA, AAI, All, IAI. The
rule that the major must be universal excludes OAO.
OF THE DETERMINA TION OF THE MOODS, ETC. 1 95
Thus we are left with six moods which are valid in the
second figure, namely,
EAE. AEE. EIO. AGO. EAO. AEO.
FIGURE III.
§ 625. The rule that the conclusion must be particular
confines us to eight moods, two of which, namely AE1£)
and AOO, are excluded by the rule that the minor premiss
must be affirmative.
Thus we are left with six moods which are valid in the
third figure, namely,
AAL IAI. AIL EAO. OAO. EIO.
FIGURE IV.
§ 626. The first of the eleven moods, AAA, is excluded
by the rule that the conclusion cannot be a universal
affirmative.
Two more moods, namely AOO and OAO, are excluded
by the rule that neither of the premisses can be a par
ticular negative.
All violates the rule that when the major premiss is
affirmative, the minor must be universal.
EAE violates the rule that, when the minor premiss
is affirmative, the conclusion must be particular.
Thus we are left with six moods which are valid in the
fourth figure, namely,
AAL AEE. IAI. EAO. EIO, AEO.
§ 627. Thus the 256 possible forms of syllogism have
o 2
196 OF THE DETERMINATION OF THE MOODS
been reduced to two dozen legitimate combinations of
mood and figure, six moods being valid in each of the
four figures.
FIGURE I. AAA. EAE. AIL EIO. (AAI. EAO.)
FIGURE II. EAE. AEE. EIO. AGO. (EAO. AEO.)
FIGURE III. AAI. IAI. AIL EAO. OAO. EIO.
FIGURE IV. AAI. AEE. IAI. EAO. EIO. (AEO.)
§ 628. The five moods enclosed in brackets, though
valid, are useless. For the conclusion drawn is less than
is warranted by the premisses. These are called Subaltern
Moods, because their conclusions might be inferred by
subalternation from the universal conclusions which can
justly be drawn from the same premisses. Thus AAI is
subaltern to AAA, EAO to EAE, and so on with the rest.
§ 629. The remaining 19 combinations of mood and
figure, which are loosely called ' moods/ though in
strictness they should be called ' figured moods,' are
generally spoken of under the names supplied by the
following mnemonics —
Barbara, Celarent, Darii, Ferioque prioris ;
Cesare, Camestres, Festino, Baroko secundre ;
Tertia Darapti, Disamis, Datisi, Felapton,
Bokardo, Ferison habet ; Quarta insuper addit
Bramantip, Camenes, Dimaris, Fesapo, Fresison :
Quinque Subaltern!, totidem Generalibus orti,
Nomen habent nullum, nee, si bene colligis, usum.
§ 630. The vowels in these lines indicate the letters of
the mood. All the special rules of the four figures can be
THAT ARE VALID IN THE FOUR FIGURES. 197
gathered from an inspection of them. The following
points should be specially noted.
The first figure proves any kind of conclusion, and is
the only one which can prove A.
The second figure proves only negatives.
The third figure proves only particulars.
The fourth figure proves any conclusion except A.
§ 631. The first figure is called the Perfect, and the rest
the Imperfect figures. The claim of the first to be
regarded as the perfect figure may be rested on these
grounds —
1. It alone conforms directly to the Dictum de Omni
et Nullo.
2. It suffices to prove every kind of conclusion, and
is the only figure in which a universal affirma
tive proposition can be established.
3. It is only in a mood of this figure that the major,
middle and minor terms are to be found stand
ing in their relative order of extension.
§ 632. The reason why a universal affirmative, which is
of course infinitely the most important form of proposition,
can only be proved in the first figure may be seen as
follows.
Proof that A can only be established in figure I.
An A conclusion necessitates both premisses being A
propositions (by Rule 7). But the minor term is distributed
in the conclusion, as being the subject of an A proposition .
and must therefore be distributed in the minor premiss, in
order to which it must be the subject. Therefore the
198 OF THE DE TERMINA TION OF THE MO ODS, E TC.
middle term must be the predicate and is consequently un
distributed. In order therefore that the middle term may
be distributed, it must be subject in the major premiss,
since that also is an A proposition. But when the middle
term is subject in the major and predicate in the minor
premiss, we have what is called the first figure.
CHAPTER XV.
Of the Special Canons of the Four Figures.
§ 633. So far we have given only a negative test of
legitimacy, having shown what moods are not invalidated
by running counter to any of the special rules of the four
figures. We will now lay down special canons for the
four figures, conformity to which will serve as a positive
test of the validity of a given mood in a given figure. The
special canon of the first figure will of course be practically
equivalent to the Dictum de Omni et Nullo. All of them
will be expressed in terms of extension, for the sake of
perspicuity.
Special Canons of the Four Figures.
FIGURE I.
§ 634. CANON. If one term wholly includes or excludes
another, which wholly or partly includes a
third, the first term wholly or partly includes
or excludes the third.
2OO
OF THE SPECIAL CANONS
Here four cases arise —
(i) Total inclusion (Barbara).
All B is A.
All C is B.
.-. All C is A.
(2) Partial inclusion (Darii).
All B is A.
Some C is B.
Some C is A.
(3) Total exclusion (Celarent).
No B is A.
All C is B.
No C is A.
OF THE FOUR FIGURES.
(4) Partial exclusion (Ferio).
201
No B is A.
Some C is B.
Some C is not A.
FIGURE II.
§ 635. CANON. If one term is excluded from another,
which wholly or partly includes a third, or is
included in another from which a third is
wholly or partly excluded, the first is excluded
from the whole or part of the third.
Here we have four cases, all of exclusion —
(i) Total exclusion on the ground of inclusion in an
excluded term (Cesare).
No A is B.
All C is B.
No C is A.
2O2
OF THE SPECIAL CANONS
(2) Partial exclusion on the ground of a similar partial
inclusion (Festino).
No A is B.
Some C is B.
. • . Some C is not A.
(3) Total exclusion on the ground of exclusion from
an including term (Camestres).
All A is B.
No C is B.
.-. No C is A.
OF THE FOUR FIGURES.
203
(4) Partial exclusion on the ground of a similar
partial exclusion (Baroko).
All A is B.
Some C is not B.
Some C is not A.
FIGURE III.
636. CANON. If two terms include another term in
common, or if the first includes the whole
and the second a part of the same term, or
vice versa, the first of these two terms partly
includes the second ; and if the first is excluded
from the whole of a term which is wholly
or in part included in the second, or is
excluded from part of a term which is wholly
included in the second, the first is excluded
from part of the second.
Here it is evident from the statement that six
cases arise —
204
OF THE SPECIAL CANONS
(i) Total inclusion of the same term in two others
(Darapti).
All B is A.
All B is C.
. Some C is A.
(2) Total inclusion in the first and partial inclusion
in the second (Datisi).
All B is A.
Some B is C.
. Some C is A.
OF THE FOUR FIGURES.
205
(3) Partial inclusion in the first and total inclusion in
the second (Disamis).
Some B is A.
All B is C.
. • . Some C is A.
(4) Total exclusion of the first from a term which is
wholly included in the second (Felapton).
No B is A.
All B is C.
. • . Some C is not A.
2O6
OF THE SPECIAL CANONS
(5) Total exclusion of the first from a term which is
partly included in the second (Ferison).
No B is A.
Some B is C.
. • . Some C is not A.
OF THE FOUR FIGURES.
207
(6) Exclusion of the first from part of a term which
is wholly included in the second (Bokardo).
Some B is not A.
All B is C.
. Some C is not A.
FIGURE IV.
637. CANON. If one term is wholly or partly included
in another which is wholly included in or
excluded from a third, the third term wholly
or partly includes the first, or, in the case of
total inclusion, is wholly excluded from it ;
and if a term is excluded from another which
is wholly or partly included in a third, the
third is partly excluded from the first.
208
OF THE SPECIAL CANOATS
Here we have five cases —
(i) Of the inclusion of a whole term (Bramantip),
All A is B.
All B is C.
. • . Some C is (all) A.
(2) Of the inclusion of part of a term (Dimaris).
B
Some A is B.
All B is C.
. Some C is (some) A.
OF THE FOUR FIGURES. 309
(3) Of the exclusion of a whole term (Camenes).
All A is B.
No B is C.
. No C is A.
(4) Partial exclusion on the ground of including
the whole of an excluded term (Fesapo).
No A is B.
All B is C.
Some C is not A.
210
OF THE SPECIAL CANONS
(5) Partial exclusion on the ground of including
part of an excluded term (Fresison).
No A is B.
Some B is C.
. • . Some C is not A.
§ 638. It is evident from the diagrams that in the
subaltern moods the conclusion is not drawn directly
from the premisses, but is an immediate inference from
the natural conclusion. Take for instance AAI in the
first figure. The natural conclusion from these premisses
OF THE FOUR FIGURES.
211
is that the minor term C is wholly contained in the major
term A. But instead of drawing this conclusion we go on
to infer that something which is contained in C, namely
some C, is contained in A.
All B is A.
All C is B.
. All C is A.
. Some C is A.
Similarly in EAO in figure I, instead of arguing that
the whole of C is excluded from A, we draw a conclusion
which really involves a further inference, namely that part
of C is excluded from A.
No B is A.
All C is B.
. No C is A.
. Some C is not A.
§ 639. The reason why the canons have been ex
pressed in so cumbrous a form is to render the validity of
all the moods in each figure at once apparent from the
p 2
212 OF THE SPECIAL CANONS
statement. For purposes of general convenience they
admit of a much more compendious mode of expression.
§ 640. The canon of the first figure is known as the
Dictum de Omni et Nullo —
What is true (distributively) of a whole term is true of
all that it includes.
§ 641. The canon of the second figure is known as the
Dictum de Diverso —
If one term is contained in, and another excluded from,
a third term, they are mutually excluded.
§ 642. The canon of the third figure is known as the
Dictum de Exemplo et de Excepto —
Two terms which contain a common part partly agree,
or, if one contains a part which the other does not, they
partly differ.
§ 643. The canon of the fourth figure has had no
name assigned to it, and does not seem to admit of
any simple expression. Another mode of formulating it
is as follows :—
Whatever is affirmed of a whole term may have par
tially affirmed of it whatever is included in that term
(Bramantip, Dimaris), and partially denied of it whatever
is excluded (Fesapo) ; whatever is affirmed of part of a
term may have partially denied of it whatever is wholly
excluded from that term (Fresison) ; and whatever is denied
of a whole term may have wholly denied of it whatever is
wholly included in that term (Camenes).
§ 644. From the point of view of intension the canons
of the first three figures may be expressed as follows.
OF THE FOUR FIGURES. 213
§ 645. Canon of the first figure. Dictum de Omni et
Nullo—
An attribute of an attribute of anything is an attribute
of the thing itself.
§ 646. Canon of the second figure. Dictum deDiverso —
If a subject has an attribute which a class has not, or
vice versa, the subject does not belong to the class.
§ 647. Canon of the third figure.
I. Dictum de Exemplo —
If a certain attribute can be affirmed of any portion of
the members of a class, it is not incompatible with the
distinctive attributes of that class.
II. Dictum de Excepto —
If a certain attribute can be denied of any portion of
the members of a class, it is not inseparable from the
distinctive attributes of that class.
CHAPTER XVI.
Of the Special Uses of the Four Figures.
§ 648. THE first figure is useful for proving the proper
ties of a thing.
§ 649. The second figure is useful for proving distinc
tions between things.
§ 650. The third figure is useful for proving instances
or exceptions.
§ 651. The fourth figure is useful for proving the
species of a genus.
FIGURE I.
§ 652. B is or is not A.
CisB.
. • . C is or is not A.
We prove that C has or has not the property A by
predicating of it B, which we know to possess or not to
possess that property.
Luminous objects are material.
Comets are luminous.
. • . Comets are material.
No moths are butterflies.
The Death's head is a moth.
. • . The Death's head is not a butterfly.
OF THE SPECIAL USES OF THE FOUR FIGURES. 2 15
FIGURE II.
§ 653. A is B. A is not B.
C is not B. C is B.
. • . C is not A. . • . C is not A.
We establish the distinction between C and A by show
ing that A has an attribute which C is devoid of, or is devoid
of an attribute which C has.
All fishes are cold-blooded.
A whale is not cold-blooded.
. • . A whale is not a fish.
No fishes give milk.
A whale gives milk.
. • . A whale is not a fish.
FIGURE III.
§ 654. B is A. B is not A.
B is C. B is C.
. • . Some C is A. . • . Some C is not A.
We produce instances of C being A by showing that C
and A meet, at all events partially, in B. Thus if we
wish to produce an instance of the compatibility of
great learning with original powers of thought, we might
say-
Sir William Hamilton was an original thinker.
Sir William Hamilton was a man of great learning.
. . Some men of great learning are original thinkers.
Or we might urge an exception to the supposed rule
2l6 OF THE SPECIAL USES OF THE FOUR FIGURES.
about Scotchmen being deficient in humour under the
same figure, thus —
Sir Walter Scott was not deficient in humour.
Sir Walter Scott was a Scotchman.
. • . Some Scotchmen are not deficient in humour.
FIGURE IV.
§ 655. All A is B. No A is B.
All B is C. All B is C.
. • . Some C is A. . • . Some C is not A.
We show here that A is or is not a species of C by
showing that A falls, or does not fall, under the class B,
which itself falls under C. Thus-
All whales are mammals.
All mammals are warm-blooded.
. • . Some warm-blooded animals are whales.
No whales are fishes.
All fishes are cold-blooded.
. • . Some cold-blooded animals are not whales.
CHAPTER XVII.
Of the Syllogism with three Figures.
§ 656. IT will be remembered that in beginning to
treat of figure (§ 565) we pointed out that there were
either four or three figures possible according as the
conclusion was assumed to be known or not. For, if the
conclusion be not known, we cannot distinguish between
the major and the minor term, nor, consequently, between
one premiss and another. On this view the first and the
fourth figures are the same, being that arrangement of the
syllogism in which the middle term occupies a different
position in one premiss from what it does in the other.
We will now proceed to constitute the legitimate moods
and figures of the syllogism irrespective of the con
clusion.
§ 657. When the conclusion is set out of sight, the
number of possible moods is the same as the number
of combinations that can be made of the four things,
A, E, I, O, taken two together, without restriction as to
repetition. These are the following 16 : —
AA EA IA OA
AE 4^E- IE -OS
AI El -H- -0f
AO -EG- -le- -ee-
3i8
OF THE SYLLOGISM
of which seven may be neglected as violating the general
rules of the syllogism, thus leaving us with nine valid
moods —
AA. AE. AI. AO. EA. EL IA, IE. OA.
§ 658. We will now put these nine moods successively
into the three figures. By so doing it will become
apparent how far they are valid in each.
§ 659. Let it be premised that
when the extreme in the premiss that stands first is
predicate in the conclusion, we are said to have
a Direct Mood ;
when the extreme in the premiss that stands second
is predicate in the conclusion, we are said to
have an Indirect Mood.
§ 660.
Mood A A.
FIGURE I.
Mood AE.
Mood AI.
All B is A.
All C is B.
.-. All C is A,
or Some A is C,
All B is A.
No C is B.
. • . Illicit Process,
or Some A is not C,
All B is A.
Some C is B.
. • . Some C is A,
or Some A is C.
(Barbara & Bramantip). (Fesapo).
Mood AO.
Mood EA.
(Darii & Disarms).
Mood El.
All B is A.
Some C is not B.
Illicit Process,
No B is A.
All C is B.
. • . No C is A,
or No A is C,
No B is A.
Some C is B.
. • . Some C is not A,
(Ferio),
or Illicit Process.
(Celarent & Camenes).
WITH THREE FIGURES. 31 9
Mood IA.
Mood IE.
Mood OA.
Some B is A.
Some B is C.
Some B is not A.
All C is B.
No A is B.
All C is B.
. • . Undistributed
. • . Illicit Process,
' . Undistributed
Middle.
or Some C is not A,
Middle.
(Fresison).
§ 661. Thus we are left with six valid moods, which
yield four direct conclusions and five indirect ones, cor
responding to the four moods of the original first figure
and the five moods of the original fourth, which appear
now as indirect moods of the first figure.
§ 662. But why, it maybe asked, should not the moods
of the first figure equally well be regarded as indirect
moods of the fourth ? For this reason — that all the
moods of the fourth figure can be elicited out of premisses
in which the terms stand in the order of the first, whereas
the converse is not the case. If, while retaining the quan
tity and quality of the above premisses, i. e. the mood, we
were in each case to transpose the terms, we should find
that we were left with five valid moods instead of six,
since AI in the reverse order of the terms involves undis
tributed middle ; and, though we should have Celarent
indirect to Camenes, and Darii to Dimaris, we should
never arrive at the conclusion of Barbara or have any
thing exactly equivalent to Ferio. In place of Barbara,
Bramantip would yield as an indirect mood only the
subaltern AAI in the first figure. Both Fesapo and
Fresison would result in an illicit process, if we attempted
to extract the conclusion of Ferio from them as an indi-
220
OF THE SYLLOGISM
rect mood. The nearest approach we could make to
Ferio would be the mood EAO in the first figure, which
may be elicited indirectly from the premisses of Camenes,
being subaltern to Celarent. For these reasons the
moods of the fourth figure are rightly to be regarded as
indirect moods of the first, and not vice versa.
§663.
FIGURE II.
Mood A A.
Mood AE.
Mood AL
All A is B.
All C is B.
, * . Undistributed
Middle.
All A is B.
No C is B.
. • . No C is A,
or No A is C,
(Camestres & Cesare).
All A is B.
Some C is B.
• . Undistributed
Middle.
Mood AO.
Mood EA.
Mood EL
All A is B.
Some C is not
. • . Some C is not
(Baroko),
or Illicit Process.
No A is B.
B. All C is B.
A, . • . No C is A, v .
or No A is C,
(Cesare & Camestres). or
No A is B.
Some C is B.
Some C is not A,
(Festino),
Illicit Process.
Mood I A.
Mood IE.
Mood OA.
Some A is B.
All C is B.
. ' . Undistributed
Middle.
Some A is B.
No C is B.
. • . Illicit Process,
or Some A is not C, or
Some A is not B.
All C is B.
Illicit Process,
Some A is not C.
§ 664. Here again we have six valid moods, which
yield four direct conclusions corresponding to Cesare,
Camestres, Festino and Baroko. The same four are
repeated in the indirect moods.
WITH THREE FIGURES.
221
§ 665.
FIGURE III.
Mood A A.
Mood AE.
Mood AL
All B is A.
All B is A.
All B is A.
All B is C.
No B is C.
Some B is C.
. • . Some C is A,
. • . Illicit Process,
. • . Some C is A,
or Some A is C,
or Some A is not C,
or Some A is C,
(Darapti).
(Felapton).
(Datisi & Disamis).
Mood AO.
Mood EA.
Mood EL
All B is A.
No B is A.
No B is A.
Some B is not C.
All B is C.
Some B is C.
. • . Illicit Process,
. • . Some C is not A,
. ' . Some C is not A,
or Some A is not C,
(Felapton),
(Ferison),
(Bokardo).
or Illicit Process.
or Illicit Process.
Mood I A.
Mood IE.
Mood OA.
Some B is A.
Some B is A.
Some B is not A.
All B is C.
No B is C.
All B is C.
. • . Some C is A,
. • . Illicit Process,
. • . Some C is not A,
or Some A is C,
or Some A is not C,
(Bokardo),
(Disamis & Datisi).
(Ferison).
or Illicit Process.
§ 666. In this figure every mood is valid, either directly
or indirectly. We have six direct moods, answering to
Darapti, Disamis, Datisi, Felapton, Bokardo and
Ferison, which are simply repeated by the indirect moods,
except in the case of Darapti, which yields a conclusion
not provided for in the mnemonic lines. Darapti, though
going under one name, has as much right to be considered
two moods as Disamis and Datisi.
CHAPTER XVIII.
Of Reduction.
§ 667. WE revert now to the standpoint of the old
logicians, who regarded the Dictum de Omni et Nullo
as the principle of all syllogistic reasoning. From this
point of view the essence of mediate inference consists in
showing that a special case, or class of cases, comes under
a general rule. But a great deal of our ordinary reasoning
does not conform to this type. It was therefore judged
necessary to show that it might by a little manipulation be
brought into conformity with it. This process is called
Reduction.
§ 668. Reduction is of two kinds —
(1) Direct or Ostensive.
(2) Indirect or Ad Impossibile.
§ 669. The problem of direct, or ostensive, reduction is
this—
Given any mood in one of the imperfect figures (II, III
and IV) how to alter the form of the premisses so as to
arrive at the same conclusion in the perfect figure, or at
one from which it can be immediately inferred. The
alteration of the premisses is effected by means of im
mediate inference and, where necessary, of transposition.
OF REDUCTION. 223
§ 670. The problem of indirect reduction, or reductio
(per deductionem) ad impossibile, is this — Given any
mood in one of the imperfect figures, to show by means
of a syllogism in the perfect figure that its conclusion
cannot be false.
§ 671. The object of reduction is to extend the sanction
of the Dictum de Omni et Nullo to the imperfect figures,
which do not obviously conform to it.
§ 672. The mood required to be reduced is called the
Reducend ; that to which it conforms, when reduced, is
called the Reduct.
Direct or Ostensive Reduction.
§ 673. In the ordinary form of direct reduction, the
only kind of immediate inference employed is conversion,
either simple or by limitation ; but the aid of permutation
and of conversion by negation and by contraposition may
also be resorted to.
§ 674. There are two moods, Baroko and Bokardo,
which cannot be reduced ostensively except by the employ
ment of some of the means last mentioned. Accordingly,
before the introduction of permutation into the scheme of
logic, it was necessary to have recourse to some other
expedient, in order to demonstrate the validity of these two
moods. Indirect reduction was therefore devised with a
special view to the requirements of Baroko and Bokardo :
but the method, as will be seen, is equally applicable to all
the moods of the imperfect figures.
§ 675. The mnemonic lines, 'Barbara, Celarent, etc./
224 OF REDUCTION.
provide complete directions for the ostensive reduction of
all the moods of the second, third, and fourth figures to
the first, with the exception of Baroko and Bokardo. The
application of them is a mere mechanical trick, which will
best be learned by seeing the process performed.
§ 676. Let it be understood that the initial consonant
of each name of a figured mood indicates that the reduct
will be that mood which begins with the same letter.
Thus the B of Bramantip indicates that Bramantip,
when reduced, will become Barbara.
§ 677. Where m appears in the name of a reducend,
we shall have to take as major that premiss which before
was minor, and vice versa — in other words, to transpose
the premisses, m stands for mutatio or metathesis.
§ 678. s, when it follows one of the premisses of a re
ducend, indicates that the premiss in question must be
simply converted; when it follows the conclusion, as in
Disamis, it indicates that the conclusion arrived at in the
first figure is not identical in form with the original con
clusion, but capable of being inferred from it by simple
conversion. Hence s in the middle of a name indicates
something to be done to the original premiss, while s at
the end indicates something to be done to the new con
clusion.
§ 679. p indicates conversion per accidens, and what
has just been said of s applies, mutatis mutandis, to p.
§ 680. k may be taken for the present to indicate that
Baroko and Bokardo cannot be reduced ostensively.
OF REDUCTION.
§ 681.
FIGURE II.
Cesare.
Celarent.
No A is B. x /
All C is B. I = 1
. • . No C is A. J 1 .
No B is A.
All C is B.
. No C is A.
Camestres
Celarent.
All A is B. i ,
No C is B. 1 = |
. • . No C is A. ) J . •
No B is C.
All A is B.
. No A is C.
. No C is A.
Festino.
No A is B. ^ ,
Some C is B. 1 = J
Some C is not A. J ( . •
Ferio.
No B is A.
Some C is B.
. Some C is not A
[Baroko]
§ 682. FIGURE III.
Darapti. Darii.
All B is A. x All B is A.
All B is C. Some C is B.
. • . Some C is A. ) I . • . Some C is A.
Disamis.
Some B is A.
All B is C.
Some C is A.
Darii.
All B is C.
Some A is B.
Some A is C.
Some C is A.
Q
226
OF REDUCTION.
Datisi.
All B is A. x
Some B is C. I =
• . Some C is A. )
Felapton.
No B is A. x
All B is C.
Some C is not- A. J
Darii.
All B is A.
Some C is B.
Some C is A.
Ferio.
No B is A.
Some C is B.
Some C is not-A.
[Bokardo].
Ferison. Ferio.
No B is A. x , No B is A.
Some B is C. > = < Some C is B.
Some C is not A. * ' . • . Some C is not A.
§ 683. FIGURE IV.
Bramantip. Barbara.
All A is B. x / All B is C.
All B is C. All A is B.
. • . Some C is A. I ( . - . All A is C.
. • . Some C is A.
Camenes
All A is B. ,
No B is C. I =
. • . No C is A. J
Celarent
No B is C.
All A is B.
No A is C.
No C is A.
OF REDUCTION.
227
Dimaris.
Darii.
Some A is B.
All B is C.
• . Some C is A.
.» All B is C.
Some A is B.
1 L • . Some A is C.
. • . Some C is A.
Fesapo.
No A is B.
All B is C.
Some C is not A.
Ferio.
^ , No B is A.
Some C is B.
' . • . Some C is not A.
Fresison.
Ferio.
No A is B.
Some B is C.
Some C is not A.
x / No B is A.
Some C is B.
' . • . Some C is not A.
§ 684. The reason why Baroko and Bokardo cannot
be reduced ostensively by the aid of mere conversion be
comes plain on an inspection of them. In both it is neces
sary, if we are to obtain the first figure, that the position of the
middle term should be changed in one premiss. But the
premisses of both consist of A and O propositions, of
which A admits only of conversion by limitation, the effect
of which would be to produce two particular premisses,
while O does not admit of conversion at all.
It is clear then that the O proposition must cease to be
O before we can get any further. Here permutation
comes to our aid; while conversion by negation enables
us to convert the A proposition, without loss of quantity,
Q 2
228 OF REDUCTION.
and to elicit the precise conclusion we require out of the
reduct of Bokardo.
(Baroko) Fanoyro. Ferio.
All A is B. N No not-B is A.
Some C is not B. V = \ Some C is not-B.
. • . Some C is not A. ' ' . . Some C is not A.
(Bokardo) Donamon. Darii.
Some B is not A. -j /• All B is C.
All B is C. Some not-A is B.
. • . Some C is not A. ) ' . • . Some not-A is C.
. • . Some C is not-A.
§ 685. In the new symbols, Fanoird and Donamon, TV
has been adopted as a symbol for permutation ; n signifies
conversion by negation. In Donamon the first n stands
for a process which resolves itself into permutation
followed by simple conversion, the second for one which
resolves itself into simple conversion followed by permuta
tion, according to the extended meaning which we have
given to the term 'conversion by negation.' If it be
thought desirable to distinguish these two processes, the
ugly symbol Doirsamosir may be adopted in place of
Donamon.
§ 686. The foregoing method, which may be called
Reduction by Negation, is no less applicable to the other
moods of the second figure than to Baroko. The
symbols which result from providing for its application
OF REDUCTION.
229
would make the second of the mnemonic lines run
thus —
Benares, Canene, Denilorr, Fano-rd secundae.
§ 687. The only other combination of mood and figure
in which it will be found available is Camenes, whose
name it changes to Canene.
§ 688. (Cesare) Benares.
No A is B. -V
All C is B. I =
. • . No C is A. J
(Camestres) Cane?re.
All A is B. i ,
NoCisB. p=±J
. • . No C is A. J I
(Festino) DeniloTr.
No A is B.
Some C is B.
. • . Some C is not A.
Barbara
All B is not-A.
All C is B.
. All C is not-A.
. No C is A.
Celarent.
No not-B is A.
All C is not-B.
. No C is A.
Darii.
All B is not-A.
Some C is B.
. Some C is not-A.
. Some C is not A.
(Camenes) Canene.
All A is B.
Celarent.
No not-B is A.
All C is not-B.
No C is A. J ( . • . No C is A.
§ 689. The following will serve as a concrete instance
of Cane-rre reduced to the first figure.
No B is C. \ =
230 OF REDUCTION.
All things of which we have a perfect idea are per
ceptions.
A substance is not a perception.
. • . A substance is riot a thing of which we have a perfect
idea.
When brought into Celarent this becomes--
No not-perception is a thing of which we have a
perfect idea.
A substance is a not-perception.
. • . No substance is a thing of which we have a perfect
idea.
§ 690. We may also bring it, if we please, into Barbara,
by permuting the major premiss once more, so as to
obtain the contrapositive of the original —
All not-perceptions are things of which we have an
imperfect idea.
All substances are not-perceptions.
. • . All substances are things of which we have an imper
fect idea.
Indirect Reduction.
§ 691. We will apply this method to Baroko.
All A is B. All fishes are oviparous.
Some C is not B. Some marine animals are not
oviparous.
. • . Some C is not A. . • . Some marine animals are not
fishes.
§ 692. The reasoning in such a syllogism is evidently
conclusive : but it does not conform, as it stands, to the
OF REDUCTION. 231
first figure, nor (permutation apart) can its premisses be
twisted into conformity with it. But though we cannot
prove the conclusion true in the first figure, we can employ
that figure to prove that it cannot be false, by showing that
the supposition of its falsity would involve a contradiction of
one of the original premisses, which are true ex hypothesi.
§ 693. If possible, let the conclusion ' Some C is not A '
be false. Then its contradictory 'All C is A' must be
true. Combining this as minor with the original major,
we obtain premisses in the first figure,
All A is B, All fishes are oviparous,
All C is A, All marine animals are fishes,
which lead to the conclusion
All C is B, All marine animals are oviparous.
But this conclusion conflicts with the original minor,
' Some C is not B/ being its contradictory. But the
original minor is ex hypothesi true. Therefore the new
conclusion is false. Therefore it must either be wrongly
drawn or else one or both of its premisses must be false.
But it is not wrongly drawn ; since it is drawn in the first
figure, to which the Dictum de Omni et Nullo applies.
Therefore the fault must lie in the premisses. But the
major premiss, being the same with that of the original
syllogism, is ex hypothesi true. Therefore the minor
premiss, 'All C is A/ is false. But this being false, its
contradictory must be true. Now its contradictory is the
original conclusion, ' Some C is not A,' which is therefore
proved to be true, since it cannot be false.
232 OF REDUCTION.
§ 694. It is convenient to represent the two syllogisms
in juxtaposition thus —
Baroko. Barbara.
All A is B. All A is B.
Some C is not B. ^^. All C is A.
. • . Some C is not A. " - . • . All C is B.
§ 695. The lines indicate the propositions which conflict
with one another. The initial consonant of the names
Baroko and Bokardo indicates that the indirect reduct
will be Barbara. The k indicates that the O proposition,
which it follows, is to be dropped out in the new syllo
gism, and its place supplied by the contradictory of the old
conclusion.
§ 696. In Bokardo the two syllogisms will stand thus —
Bokardo. Barbara.
Some B is not A. All C is A.
All B is C. \S All B is C .
. • . Some C is not A. . • . All B is A.
§ 697. The method of indirect reduction, though in
vented with a special view to Baroko and Bokardo, is
applicable to all the moods of the imperfect figures. The
following modification of the mnemonic lines contains di
rections for performing the process in every case : —
Barbara, Celarent, Darii, Ferioque prioris ;
Felake, Dareke, Cellk6, Baroko secundae ;
Tertia Cakaci, Cikarl, Fakini, Bekaco,
Bokardo, Dekilon habet ; quarta insuper addit
Cakapl, Daseke, Cikasi, Cepak6, Cesikon.
OF REDUCTION. 233
§ 698. The c which appears in two moods of the third
figure, Cakaci and Bekaco, signifies that the new con
clusion is the contrary, instead of, as usual, the contradic
tory of the discarded premiss.
§ 699. The letters s and p, which appear only in the
fourth figure, signify that the new conclusion does not
conflict directly with the discarded premiss, but with its
converse, either simple or per accidens, as the case may
be.
§ 700. 1, n and r are meaningless, as in the original
lines.
CHAPTER XIX.
Of Immediate Inference as applied to
Complex Propositions.
§ 701. So far we have treated of inference, or reasoning,
whether mediate or immediate, solely as applied to simple
propositions. But it will be remembered that we divided
propositions into simple and complex. It becomes
incumbent upon us therefore to consider the laws of
inference as applied to complex propositions. Inasmuch
however as every complex proposition is reducible to a
simple one, it is evident that the same laws of inference
must apply to both.
§ 702. We must first make good this initial statement
as to the essential identity underlying the difference of
form between simple and complex propositions.
§ 703. Complex propositions are either Conjunctive or
Disjunctive (§ 214).
§ 704. Conjunctive propositions may assume any of the
four forms, A, E, I, O, as follows—
(A) If A is B, C is always D.
(E) If A is B, C is never D.
(I) If A is B, C is sometimes D.
(O) If A is B, C is sometimes not D.
OF IMMEDIATE INFERENCE, ETC. 235
§ 705. These admit of being read in the form of simple
propositions, thus —
(A) If A is B, C is always D= All cases of A being B
are cases of C being D. (Every AB is a
CD.)
(E) If A is B, C is never D = No cases of A being B
are cases of C being D. (No AB is a
CD.)
(I) If A is B, C is sometimes D = Some cases of A
being B are cases of C being D. (Some
AB's are CD's.)
(0) If A is B, C is sometimes not D=Some cases of
A being B are not cases of C being D.
(Some AB's are not CD's.)
§ 706. Or, to take concrete examples,
(A) If kings are ambitious, their subjects always
suffer.
= All cases of ambitious kings are cases of subjects
suffering.
(E) If the wind is in the south, the river never
freezes.
— No cases of wind in the south are cases of the
river freezing.
(1) If a man plays recklessly, the luck sometimes
goes against him.
= Some cases of reckless playing are cases of luck
going against one.
236 OF IMMEDIATE INFERENCE AS APPLIED
(O) If a novel has merit, the public sometimes do
not buy it.
= Some cases of novels with merit are not cases
of the public buying.
§ 707. We have seen already that the disjunctive differs
from the conjunctive proposition in this, that in the con
junctive the truth of the antecedent involves the truth of
the consequent, whereas in the disjunctive the falsity of
the antecedent involves the truth of the consequent.
The disjunctive proposition therefore
Either A is B or C is D
may be reduced to a conjunctive
If A is not B, C is D,
and so to a simple proposition with a negative term for
subject.
All cases of A not being B are cases of C being D.
(Every not-AB is a CD.)
§ 708. It is true that the disjunctive proposition, more
than any other form, except U, seems to convey two
statements in one breath. Yet it ought not, any more than
the E proposition, to be regarded as conveying both with
equal directness. The proposition ' No A is B ' is not
considered to assert directly, but only implicitly, that ' No
B is A.' In the same way the form ' Either A is B or C
is D ' ought to be interpreted as meaning directly no more
than this, ' If A is not B, C is D.' It asserts indeed by
implication also that ' If C is not D, A is B.' But this is
an immediate inference, being, as we shall presently see.
TO COMPLEX PROPOSITIONS. 237
the contrapositive of the original. When we say ' So and
so is either a knave or a fool/ what we are directly
asserting is that, if he be not found to be a knave, he will
be found to be a fool. By implication we make the
further statement that, if he be not cleared of folly, he will
stand condemned of knavery. This inference is so
immediate that it seems indistinguishable from the former
proposition : but since the two members of a complex
proposition play the part of subject and predicate, to say
that the two statements are identical would amount to
asserting that the same proposition can have two subjects
and two predicates. From this point of view it becomes
clear that there is no difference but one of expression
between the disjunctive and the conjunctive proposition.
The disjunctive is merely a peculiar way of stating a
conjunctive proposition with a negative antecedent.
709. Conversion of Complex Propositions.
f If A is B, Cis
t . • . If C is D, A is
If A is B, C is always D.
sometimes B.
f If A is B, C is never D.
I . • . If C is D, A is never B.
f If A is B, C is sometimes D.
L . • . If C is D, A is sometimes B.
§ 710. Exactly the same rules of conversion apply to
conjunctive as to simple propositions.
§ 711. A can only be converted per accidens, as
above.
238 OF IMMEDIATE INFERENCE AS APPLIED
The original proposition
< If A is B, C is always D '
is equivalent to the simple proposition
' All cases of A being B are cases of C being D.'
This, when converted, becomes
' Some cases of C being D are cases of A being B/
which, when thrown back into the conjunctive form,
becomes
' If C is D, A is sometimes B/
§ 712. This expression must not be misunderstood as
though it contained any reference to actual existence.
The meaning might be better conveyed by the form
'If C is D, A maybe B.'
But it is perhaps as well to retain the other, as it serves to
emphasize the fact that formal logic is concerned only
with the connection of ideas.
§ 713. A concrete instance will render the point under
discussion clearer. The example we took before of an
A proposition in the conjunctive form —
' If kings are ambitious, their subjects always suffer '
may be converted into
' If subjects suffer, it may be that their kings are
ambitious/
i.e. among the possible causes of suffering on the part of
subjects is to be found the ambition of their rulers, even
if every actual case should be referred to some other
cause. It is in this sense only that the inference is a
necessary one. But then this is the only sense which
TO COMPLEX PROPOSITIONS. 239
formal logic is competent to recognise. To judge of
conformity to fact is no part of its province. From
' Every AB is a CD ' it follows that ' Some CD's are
AB's ' with exactly the same necessity as that with which
' Some B is A ' follows from ' All A is B.' In the latter
case also neither proposition may at all conform to fact.
From ' All centaurs are animals ' it follows necessarily
that ' Some animals are centaurs ' : but as a matter of fact
this is not true at all.
§ 714. The E and the I proposition may be converted
simply, as above.
§ 715. O cannot be converted at all. From the propo
sition
' If a man runs a race, he sometimes does not win it,'
it certainly does not follow that
1 If a man wins a race, he sometimes does not run it.'
§ 716. There is a common but erroneous notion that
all conditional propositions are to be regarded as affirma
tive. Thus it has been asserted that, even when we say
that ' If the night becomes cloudy, there will be no dew,'
the proposition is not to be regarded as negative, on the
ground that what we affirm is a relation between the
cloudiness of night and the absence of dew. This is a
possible, but wholly unnecessary, mode of regarding the
proposition. It is precisely on a par with Hobbes's theory
of the copula in a simple proposition being always affirma
tive. It is true that it may always be so represented at
the cost of employing a negative term ; and the same is
the case here.
240 OF IMMEDIATE INFERENCE AS APPLIED
§ 717. There is no way of converting a disjunctive
proposition except by reducing it to the conjunctive form.
§ 718. Permutation of Complex Propositions.
(A) If A is B, C is always D.
. • . If A is B, C is never not-D. (E)
(E) If A is B, C is never D.
. • . If A is B, C is always not-D. (A)
(I) If A is B, C is sometimes D.
. • . If A is B, C is sometimes not not-D. (O)
(0) If A is B, C is sometimes not D.
. • . If A is B, C is sometimes not-D. (I)
§ 719. (A) If a mother loves her children, she is
always kind to them.
. • . If a mother loves her children, she is never
unkind to them. (E)
(E) If a man tells lies, his friends never trust
him.
. • . If a man tells lies, his friends always distrust
him. (A)
(1) If strangers are confident, savage dogs are
sometimes friendly.
. • . If strangers are confident, savage dogs are
sometimes not unfriendly. (O)
(O) If a measure is good, its author is sometimes
not popular.
. • . If a measure is good, its author is sometimes
unpopular. (I)
TO COMPLEX PROPOSITIONS. 241
§ 720. The disjunctive proposition may be permuted as
it stands without being reduced to the conjunctive form.
Either A is B or C is D.
. • . Either A is B or C is not not-D.
Either a sinner must repent or he will be damned.
. • . Either a sinner must repent or he will not be
saved.
§ 721. Conversion by Negation of Complex Propositions.
(A) If A is B, C is always D.
. • . If C is not-D, A is never B. (E)
(E) If A is B, C is never D.
. • . If C is D, A is always not-B. (A)
(I) If A is B, C is sometimes D.
. • . If C is D, A is sometimes not not-B. (O)
(O) If A is B, C is sometimes not D.
. • . If C is not-D, A is sometimes B. (I)
(E per ace.) If A is B, C is never D.
. • . If C is not.-D, A is sometimes B. (I)
(A per ace.) If A is B, C is always D.
. • . If C is D, A is sometimes not not-D. (O)
§ 722. (A) If a man is a smoker, he always drinks.
. • . If a man is a total abstainer, he never
smokes. (E)
(E) If a man merely does his duty, no one ever
thanks him.
. • . If people thank a man, he has always done
more than his duty. (A)
R
242 OF IMMEDIATE INFERENCE AS APPLIED
(I) If a statesman is patriotic, he sometimes
adheres to a party.
. • . If a statesman adheres to a party, he is
sometimes not unpatriotic. (O)
(0) If a book has merit, it sometimes does not
sell.
. • . If a book fails to sell, it sometimes has
merit. (I)
(E per ace.) If the wind is high, rain never falls.
. • . If rain falls, the wind is sometimes high. (I)
(A per ace.) If a thing is common, it is always cheap.
. • . If a thing is cheap, it is sometimes not un
common. (O)
§ 723. When applied to disjunctive propositions, the
distinctive features of conversion by negation are still
discernible. In each of the following forms of inference
the converse differs in quality from the convertend and
has the contradictory of one of the original terms
(§ 515).
§ 724. (A) Either A is B or C is always D.
. * . Either C is D or A is never not-B. (E)
(E) Either A is B or C is never D.
. • . Either C is not-D or A is always B. (A)
(1) Either A is B or C is sometimes D.
. • . Either C is not-D or A is sometimes not B.
(O)
(O) Either A is B or C is sometimes not D.
. * . Either C is D or A is sometimes not-B. (I)
TO COMPLEX PROPOSITIONS. 243
§ 725. (A) Either miracles are possible or every ancient
historian is untrustworthy.
. • . Either ancient historians are untrustworthy
or miracles are not impossible. (E)
(E) Either the tide must turn or the vessel can
not make the port.
. • . Either the vessel cannot make the port or
the tide must turn. (A)
(I) Either he aims too high or the cartridges are
sometimes bad.
. • . Either the cartridges are not bad or he some
times does not aim too high. (O)
(O) Either care must be taken or telegrams will
sometimes not be correct.
. * . Either telegrams are correct or carelessness
is sometimes shown. (I)
§ 726. In the above examples the converse of E looks as
if it had undergone no change but the mere transposition of
the alternative. This appearance arises from mentally read
ing the E as an A proposition : but, if it were so taken, the
result would be its contrapositive, and not its converse
by negation.
§ 727. The converse of I is a little difficult to grasp.
It becomes easier if we reduce it to the equivalent con
junctive —
' If the cartridges are bad, he sometimes does not aim
too high.'
R 2
244 OF IMMEDIATE INFERENCE AS APPLIED
Here, as elsewhere, 'sometimes' must not be taken to
mean more than ' it may be that.'
§ 728. Conversion by Contraposition of Complex
Propositions.
As applied to conjunctive propositions conversion by
contraposition assumes the following forms —
(A) If A is B, C is always D.
. • . If C is not-D, A is always not-B.
(O) If A is B, C is sometimes not D.
. • . If C is not-D, A is sometimes not not-B.
(A) If a man is honest, he is always truthful.
. • . If a man is untruthful, he is always dishonest.
(O) If a man is hasty, he is sometimes not male
volent.
. • . If a man is benevolent, he is sometimes not
unhasty.
§ 729. As applied to disjunctive propositions conversion
by contraposition consists simply in transposing the two
alternatives.
(A) Either A is B or C is D.
. • . Either C is D or A is B.
For, when reduced to the conjunctive shape, the reasoning
would run thus —
If A is not B, C is D,
. • . If C is not D, A is B,
TO COMPLEX PROPOSITIONS. 245
which is the same in form as
All not- A is B.
. • . All not-B is A.
Similarly in the case of the O proposition
(O) Either A is B or C is sometimes not D.
. • . Either C is D or A is sometimes not B.
§ 730. On comparing these results with the converse
by negation of each of the same propositions, A and O,
the reader will see that they differ from them, as was to
be expected, only in being permuted. The validity of the
inference may be tested, both here and in the case of con
version by negation, by reducing the disjunctive proposi
tion to the conjunctive, and so to the simple form, then
performing the process as in simple propositions, and
finally throwing the converse, when so obtained, back into
the disjunctive form. We will show in this manner that
the above is really the contrapositive of the O proposition.
(0) Either A is B or C is sometimes not D.
= If A is not B, C is sometimes not D.
= Some cases of A not being B are not cases
of C being D. (Some A is not B.)
= Some cases of C not being D are not cases
of A being B. (Some not-B is not
not-A.)
= If C is not D, A is sometimes not B.
= Either C is D or A is sometimes not B.
CHAPTER XX.
Of Complex Syllogisms.
§ 731. A COMPLEX Syllogism is one which is composed,
in whole or part, of complex propositions.
§ 732. Though there are only two kinds of complex
proposition, there are three varieties of complex syllogism.
For we may have
(1) a syllogism in which the only kind of complex
proposition employed is the conjunctive ;
(2) a syllogism in which the only kind of complex
proposition employed is the disjunctive ;
(3) a syllogism which has one premiss conjunctive
and the other disjunctive.
The chief instance of the third kind is that known as the
Dilemma.
Syllogism
Simple
(Categorical)
Complex
(Conditional)
I
Conjunctive
(Hypothetical)
Disjunctive
Dilemma.
OF COMPLEX SYLLOGISMS. 247
The Conjunctive Syllogism.
§ 733. The Conjunctive Syllogism has one or both
premisses conjunctive propositions: but if only one is
conjunctive, the other must be a simple one.
§ 734. Where both premisses are conjunctive, the con
clusion will be of the same character ; where only one is
conjunctive, the conclusion will be a simple proposition.
§ 735. Of these two kinds of conjunctive syllogisms we
will first take that which consists throughout of conjunctive
propositions.
The Wholly Conjunctive Syllogism.
§ 736. Wholly conjunctive syllogisms do not differ
essentially from simple ones, to which they are imme
diately reducible. They admit of being constructed in
every mood and figure, and the moods of the imperfect
figures may be brought into the first by following the
ordinary rules of reduction. For instance —
Cesare. Celarent.
If A is B, C is never D.
If E is F, C is always D.
. If E is F, A is never B.
If C is D, A is never B.
If E is F, C is always D.
. • . If E is F, A is never B.
If it is day, the stars never shine. \ f If the stars shine, it is never day.
If it is night, the stars always I If it is night, the stars always
shine. shine.
If it is night, it is never day. J \ . • . If it is night, it is never day.
248 OF COMPLEX SYLLOGISMS.
Disamis . Darii.
If C is D, A is sometimes B.
If C is D, E is always F.
If E is F, A is sometimes B.
If C is D, E is always F.
If A is B, C is sometimes D.
If A is B, E is sometimes F.
. • . If E is F, A is sometimes B.
If she goes, I sometimes go. \ t If she goes, he always goes.
If she goes, he always goes. > = < If I go, she sometimes goes.
• . If he goes, I sometimes go. ) ( . • . If I go, he sometimes goes.
. • . If he goes, I sometimes go.
The Partly Conjunctive Syllogism.
§ 737. It is this kind which is usually meant when the
Conjunctive or Hypothetical Syllogism is spoken of.
§ 738. Of the two premisses, one conjunctive and one
simple, the conjunctive is considered to be the major, and
the simple premiss the minor. For the conjunctive pre
miss lays down a certain relation to hold between two
propositions as a matter of theory, which is applied in the
minor to a matter of fact.
§ 739. Taking a conjunctive proposition as a major
premiss, there are four simple minors possible. For we
may either assert or deny the antecedent or the consequent
of the conjunctive.
Constructive Mood. Destructive Mood.
(i) If A is B, C is D. (2) If A is B3 C is D.
A is B. C is not D.
. • . C is D. . • . A is not B.
(3) If A is B, C is D. (4) If A is B, C is D.
A is not B. C is D.
No conclusion. No conclusion.
OF COMPLEX SYLLOGISMS. 249
§ 740. When we take as a minor ' A is not B ' (3), it is
clear that we can get no conclusion. For to say that C
is D whenever A is B gives us no right to deny that C can
be D in the absence of that condition. What we have
predicated has been merely inclusion of the case AB in
the case CD.
§ 741. Again, when we take as a minor, ' C is D ' (4),
we can get no universal conclusion. For though A being
B is declared to involve as a consequence C being D, yet
it is possible for C to be D under other circumstances, or
from other causes. Granting the truth of the proposition
' If the sky falls, we shall catch larks/ it by no means
follows that there are no other conditions under which
this result can be attained.
§ 742. From a consideration of the above four cases we
elicit the following
Canon of the Conjunctive Syllogism.
To affirm the antecedent is to affirm the consequent, and
to deny the consequent is to deny the antecedent : but
from denying the antecedent or affirming the consequent
no conclusion follows.
250 OF COMPLEX SYLLOGISMS.
§ 743. There is a case, however, in which we can
legitimately deny the antecedent and affirm the conse
quent of a conjunctive proposition, namely, when the
relation predicated between the antecedent and the conse
quent is not that of inclusion but of coincidence — where
in fact the conjunctive proposition conforms to the type u.
For example —
Denial of the Antecedent.
If you repent, then only are you forgiven.
You do not repent.
. • . You are not forgiven.
Affirmation of the Consequent.
If you repent, then only are you forgiven.
You are forgiven.
. • . You repent.
CHAPTER XXI.
Of the Red^(,ction of the Partly Conjunctive
Syllogism.
§ 744. SUCH syllogisms as those just treated of, if
syllogisms they are to be called, have a major and a middle
term visible to the eye, but appear to be destitute of a
minor. The missing minor term is however supposed to
be latent in the transition from the conjunctive to the
simple form of proposition. When we say ' A is B,' we
are taken to mean, ' As a matter of fact, A is B ' or ' The
actual state of the case is that A is B.' The insertion
therefore of some such expression as ' The case in hand,'
or * This case,' is, on this view, all that is wanted to com
plete the form of the syllogism. When reduced in this
manner to the simple type of argument, it will be found
that the constructive conjunctive conforms to the first
figure and the destructive conjunctive to the second.
Constructive Mood. Barbara.
If A is B, C is D.\ / All cases of A being B are cases of C
being D.
A is B. This is a case of A being B.
. • . C is D. ) 1. • . This is a case of C being D.
252 OF THE REDUCTION OF THE
Destructive Mood. Camestres.
If AisB, CisD.>
C is not D.
. A is not B.
All cases of A being B are cases of C
being D.
This is not a case of C being D.
. • . This is not a case of A being B.
§ 745. It is apparent from the position of the middle
term that the constructive conjunctive must fall into the
first figure and the destructive conjunctive into the second.
There is no reason, however, why they should be confined
to the two moods, Barbara and Camestres. If the infer
ence is universal, whether as general or singular, the mood
is Barbara or Camestres ; if it is particular, the mood is
Darii or Baroko.
Barbara. Camestres.
If A is B, C is always D.. If A is B, C is always D.\
A is always B.
' . C is always D,
If A is B, C is always D.
A is in this case B.
• . C is in this case D.
C is never D.
. A is never B.
If A is B, C is always D.
C is not in this case D.
. • . A is not in this case B.
Darii. Baroko.
If A is B, C is always D. If A is B, C is never D.
A is sometimes B. C is sometimes not D.
. • . C is sometimes D. . • . A is sometimes not B.
§ 746. The remaining moods of the first and second
figure are obtained by taking a negative proposition as the
consequent in the major premiss.
PARTLY CONJUNCTIVE SYLLOGISM. 253
Celarent. Ferio.
If A is B, C is never D. If A is B, C is never D.
A is always B, A is sometimes B.
. • . C is never D. . • . C is sometimes not D.
Cesare. Festino.
If A is B, C is never D. If A is B, C is never D.
C is always D. C is sometimes D.
. • . A is never B. . • . A is sometimes not B.
§ 747. As the partly conjunctive syllogism is thus
reducible to the simple form, it follows that violations of
its laws must correspond with violations of the laws of
simple syllogism. By our throwing the illicit moods into
the simple form it will become apparent what fallacies are
involved in them.
Denial of Antecedent.
If A is B, C is D.\ ( All cases of A being B are cases of C
being D.
A is not B. I = 1 Tllis is not a case of A being B.
.-.CisnotD. J I.-. This is not a case of C being D.
Here we see that the denial of the antecedent amounts to
illicit process of the major term.
§ 748. Affirmation of Consequent.
If A is B, C is D. \ i All Cases of A being B are cases of C
being D.
C is D. ) ( This is a case of C being D.
Here we see that the affirmation of the consequent amounts
to undistributed middle.
254 OF THE REDUCTION OF THE
§ 749. If we confine ourselves to the special rules of the
four figures, we see that denial of the antecedent involves
a negative minor in the first figure, and affirmation of the
consequent two affirmative premisses in the second. Or,
if the consequent in the major premiss were itself negative,
the affirmation of it would amount to the fallacy of two
negative premisses. Thus —
If A is B, C is not D.
C is not D.
No cases of A being B are cases of C
being D.
This is not a case of C being D.
§ 750. The positive side of the canon of the conjunctive
syllogism — ' To affirm the antecedent is to affirm the
consequent/ corresponds with the Dictum de Omni. For
whereas something (viz. C being D) is affirmed in the major
of all conceivable cases of A being B, the same is affirmed
in the conclusion of something which is included therein,
namely, ' this case/ or ' some cases/ or even ' all actual
cases.'
§ 751. The negative side — 'to deny the consequent is
to deny the antecedent ' — corresponds with the Dictum de
Diverso (§ 643). For whereas in the major all conceivable
cases of A being B are included in C being D, in the
minor 'this case/ or 'some cases/ or even 'all actual
cases ' of C being D, are excluded from the same notion.
§ 752. The special characteristic of the partly conjunc
tive syllogism lies in the transition from hypothesis to fact.
We might lay down as the appropriate axiom of this form
of argument, that ' What is true in the abstract is true in
the concrete/ or ' What is true in theory is also true in fact/
PARTLY CONJUNCTIVE SYLLOGISM. 255
a proposition which is apt to be neglected or denied. But
this does not vitally distinguish it from the ordinary
syllogism. For though in the latter we think rather of the
transition from a general truth to a particular application of
it, yet at bottom a general truth is nothing but a hypothesis
resting upon a slender basis of observed fact. The propo
sition ' A is B ' may be expressed in the form ' If A is, B
is.' To say that ' All men are mortal ' may be interpreted
to mean that ' If we find in any subject the attributes of
humanity, the attributes of mortality are sure to accompany
them.'
CHAPTER XXII.
Of the Partly Conjunctive Syllogism regarded
as an Immediate Inference.
§ 753. IT is the assertion of fact in the minor premiss,
where we have the application of an abstract principle to
a concrete instance, which alone entitles the partly con
junctive syllogism to be regarded as a syllogism at all.
Apart from this the forms of semi-conjunctive reasoning
run at once into the moulds of immediate inference.
§ 754. The constructive mood will then be read in this
Way~ If A is B, C is D,
. • . A being B, C is D,
reducing itself to an instance of immediate inference by
subaltern opposition —
Every case of A being B, is a case of C being D.
. • . Some particular case of A being B is a case of C
being D.
§ 755. Again, the destructive conjunctive will read as
follows —
If A is B, CisD,
. • . C not being D, A is not B,
THE PARTLY CONJUNCTIVE SYLLOGISM, ETC. 257
which is equivalent to
All cases of A being B are cases of C being D.
. • . Whatever is not a case of C being D is not a case of
A being B.
. • . Some particular case of C not being D is not a case
of A being B.
But what is this but an immediate inference by contra
position, coming under the formula
All A is B,
. • . All not-B is not-A,
and followed by Subalternation ?
§ 756. The fallacy of affirming the consequent becomes
by this mode of treatment an instance of the vice of
immediate inference known as the simple conversion of
an A proposition. ' If A is B, C is D ' is not convertible
with ' If C is D, A is B ' any more than ' All A is B ' is
convertible with ' All B is A.'
§ 757. We may however argue in this way
If A is B, C is D,
CisD,
. • . A may be B,
which is equivalent to saying,
When A is B, C is always D,
. * . When C is D, A is sometimes B,
and falls under the legitimate form of conversion of A
per accidens —
All cases of A being B are cases of C being D.
. • . Some cases of C being D are cases of A being B.
s
258 THE PARTLY CONJUNCTIVE SYLLOGISM, ETC.
§ 758. The fallacy of denying the antecedent assumes
the following form —
If A is B, C is D,
. • . If A is not B, C is not D,
equivalent to —
All cases of A being B are cases of C being D.
. • . Whatever is not a case of A being B is not a case of
C being D.
This is the same as to argue-
All A is B,
. • . All not-A is not-B,
an erroneous form of immediate inference for which there
is no special name, but which involves the vice of simple
conversion of A, since ' All not-A is not-B ' is the contra-
positive, not of ' All A is B/ but of its simple converse
< All B is A/
§ 759. The above-mentioned form of immediate infer
ence, however (namely, the employment of contraposition
without conversion), is valid in the case of the U proposi
tion ; and so also is simple conversion. Accordingly we
are able, as we have seen, in dealing with a proposition of
that form, both to deny the antecedent and to assert the
consequent with impunity —
If A is B, then only C is D,
. • . A not being B, C is not D ;
and again, C being D, A must be B.
CHAPTER XXIII.
Of the Disjunctive Syllogism.
§ 760. ROUGHLY speaking, a Disjunctive Syllogism re
sults from the combination of a disjunctive with a simple
premiss. As in the preceding form, the complex propo
sition is regarded as the major premiss, since it lays down
a hypothesis, which is applied to fact in the minor.
§ 761. The Disjunctive Syllogism may be exactly
denned as follows —
A complex syllogism, which has for its major premiss a
disjunctive proposition, either the antecedent or consequent
of which is in the minor premiss simply affirmed or denied.
§ 762. Thus there are four types of disjunctive syllo
gism possible.
Constructive Moods.
(i) Either A is B or C is D. (2) Either A is B or C is D.
A is not B. C is not D.
. • . C is D. . • . A is B.
Either death is annihilation or we are immortal.
Death is not annihilation.
. • . We are immortal.
Either the water is shallow or the boys will be drowned.
The boys are not drowned.
. • . The water is shallow.
s 2
260 OF THE DISJUNCTIVE SYLLOGISM.
Destructive Moods.
(3) Either A is B or C is D. (4) Either A is B or C is D.
A is B. C is D.
. • . C is not D. . • . A is not B.
§ 763. Of these four, however, it is only the constructive
moods that are formally conclusive. The validity of the
two destructive moods is contingent upon the kind of
alternatives selected. If these are such as necessarily to
exclude one another, the conclusion will hold, but not
otherwise. They are of course mutually exclusive when
ever they embody the result of a correct logical division,
as ' Triangles are either equilateral, isosceles or scalene/
Here, if we affirm one of the members, we are justified in
denying the rest. When the major thus contains the
dividing members of a genus, it may more fitly be symbol
ized under the formula, ' A is either B or C/ But as this
admits of being read in the shape, ' Either A is B or A is
C/ we retain the wider expression which includes it. Any
knowledge, however, which we may have of the fact that
the alternatives selected in the major are incompatible
must come to us from material sources ; unless indeed we
have confined ourselves to a pair of contradictory terms
(A is either B or not-B). There can be nothing in the
form of the expression to indicate the incompatibility of
the alternatives, since the same form is employed when the
alternatives are palpably compatible. When, for instance,
we say, ' A successful student must be either talented or
industrious/ we do not at all mean to assert the positive
OF THE DISJUNCTIVE SYLLOGISM. 2,6 1
incompatibility of talent and industry in a successful
student, but only the incompatibility of their negatives —
in other words, that, if both are absent, no student can be
successful. Similarly, when it is said, ' Either your play
is bad or your luck is abominable/ there is nothing in the
form of the expression to preclude our conceiving that
both may be the case.
§ 764. There is no limit to the number of members in
the disjunctive major. But if there are only two alterna
tives, the conclusion will be a simple proposition ; if there
are more than two, the conclusion will itself be a disjunc
tive. Thus —
Either A is B or C is D or E is F or G is H.
E is not F.
. • . Either A is B or C is D or G is H.
§ 765. The Canon of the Disjunctive Syllogism may be
laid down as follows —
To deny one member is to affirm the rest, either simply
or disjunctively ; but from affirming any member nothing
follows.
CHAPTER XXIV.
Of the Red^iction of the Disjunctive
Syllogism.
§ 766. WE have seen that in the disjunctive syllogism
the two constructive moods alone are formally valid. The
first of these, namely, the denial of the antecedent, will
in all cases give a simple syllogism in the first figure;
the second of them, namely, the denial of the consequent,
will in all cases give a simple syllogism in the second
figure.
Denial of Antecedent =
Either A is B or C is D. ^ ( If A is not B,C is D/
A is not B.
. • . C is D
A is not B.
. C is D.
Barbara.
All cases of A not being B are
cases of C being D.
This is a case of A not being B.
This is a case of C being D.
Denial of Consequent =
Either A is B or C is. D.\ I If A is not B, C is D.
C is not D.
. • . A is B.
C is not D.
,.'. AisB. J
Camestres.
All cases of A not being B are
cases of C being D.
This is not a case of C being D.
This is not a case of A being B.
REDUCTION OF DISJUNCTIVE SYLLOGISM. 263
§ 767. The other moods of the first and second figures
can be obtained by varying the quality of the antecedent
and consequent in the major premiss and reducing the
quantity of the minor.
§ 768. The invalid destructive moods correspond with
the two invalid types of the partly conjunctive syllogism,
and have the same fallacies of simple syllogism underlying
them. Affirmation of the antecedent of a disjunctive is
equivalent to the semi-conjunctive fallacy of denying the
antecedent, and therefore involves the ordinary syllogistic
fallacy of illicit process of the major.
Affirmation of the consequent of a disjunctive is equiva
lent to the same fallacy in the semi-conjunctive form, and
therefore involves the ordinary syllogistic fallacy of undis
tributed middle.
Affirmation of Antecedent = Illicit Major.
Either A is B or C is D \ ( If A is not B, C is D.\ /' All cases of A not being B are
cases of C being D.
A is B. _J A is B. [ _J This is not a case of A not
I being B.
. • . This is not a case of C not
\ being D.
Affirmation of Consequent = Undistributed Middle,
Either A is B or C is D. \ I If A is not B, C is D. I All cases of A not being B are cases
[ = ' = j of C being D.
C is D. J ( C is D. (This is a case of C being D.
§ 769. So far as regards the consequent, the two species
of complex reasoning hitherto discussed are identical both
in appearance and reality. The apparent difference of
264 REDUCTION OF DISJUNCTIVE SYLLOGISM.
procedure in the case of the antecedent, namely, that it is
affirmed in the partly conjunctive, but denied in the dis
junctive syllogism, is due merely to the fact that in the
disjunctive proposition the truth of the consequent is in
volved in the falsity of the antecedent, so that the
antecedent being necessarily negative, to deny it in appear
ance is in reality to assert it.
CHAPTER XXV.
The Disjunctive Syllogism regarded as an
Immediate Inference.
§ 770. IF no stress be laid on the transition from
disjunctive hypothesis to fact, the disjunctive syllogism will
run with the same facility as its predecessor into the moulds
of immediate inference.
§ 771.
Denial of Antecedent.
Either A is B or C is D.
. • . A not being B, C is D.
j
§ 772.
Denial of Consequent.
Either A is B or C is D. 1
. • . C not being D, A is B.
Subalternation.
Every case of A not being B
is a case of C being D.
Some case of A not being B
is a case of C being D.
Conversion by Contraposi
tion + Subalternation.
All cases of A not being B
are cases of C being D.
• . All cases of C not being D are
cases of A being B.
• . Some case of C not being D is
a case of A being B.
266 THE DISJUNCTIVE SYLLOGISM REGARDED
§ 773. Similarly the two invalid types of disjunctive
syllogism will be found to coincide with fallacies of im
mediate inference.
§774.
Affirmation of Antecedent. Contraposition without
Conversion.
Either A is B or C is D.^ / All cases of A not being B are
cases of C being D.
- • . A being B, C is not D. [ 1 . • . All cases of A being B are
/ \ cases of C not being D.
§ 775. The affirmation of the antecedent thus comes
under the formula —
All not-A is B,
. • . All A is not-B,
a form of inference which cannot hold except where A and
B are known to be incompatible. Who, for instance,
would assent to this ? —
All non-boating men play cricket.
. • . All boating men are non-cricketers.
§776.
Affirmation of Consequent. Simple Conversion of A.
Either A is B or C is D.
. • . C being D, A is not B.
All cases of A not being B are
cases of C being D.
. All cases of C being D are
cases of A not being B.
AS AN IMMEDIATE INFERENCE. 26 J
§ 777. We may however argue in this way —
Conversion of A per accidens.
Either A is B or C is D. \ i All cases of A not being B
are cases of C being D.
. • . C being D, A is sometimes B. f 1 . • . Some cases of C being D are
J I cases of A not being B.
The men who pass this examination must have either
talent or industry.
. • . Granting that they are industrious, they may be
without talent.
CHAPTER XXVI.
Of the Mixed Form of Complex Syllogism.
§ 778. UNDER this head are included all syllogisms in
which a conjunctive is combined with a disjunctive pre
miss. The best known form is
The Dilemma.
§ 779. The Dilemma may be defined as —
A complex syllogism, having for its major premiss a
conjunctive proposition with more than one antecedent, or
more than one consequent, or both, which (antecedent or
consequent) the minor premiss disjunctively affirms or
denies.
§ 780. It will facilitate the comprehension of the
dilemma, if the following three points are borne in
mind —
(1) that the dilemma conforms to the canon of the
partly conjunctive syllogism, and therefore a
valid conclusion can be obtained only by affirm
ing the antecedent or denying the consequent ;
(2) that the minor premiss must be disjunctive ;
OF THE MIXED FORM OF COMPLEX SYLLOGISM. 269
(3) that if only the antecedent be more than one, the
conclusion will be a simple proposition ; but if
both antecedent and consequent be more than
one, the conclusion will itself be disjunctive.
§ 781. The dilemma, it will be seen, differs from the
partly conjunctive syllogism chiefly in the fact of having a
disjunctive affirmation of the antecedent or denial of the
consequent in the minor, instead of a simple one. It
is this which constitutes the essence of the dilemma, and
which determines its possible varieties. For if only the
antecedent or only the consequent be more than one, we
must, in order to obtain a disjunctive minor, affirm the
antecedent or deny the consequent respectively ; whereas,
if there be more than one of both, it is open to us to take
either course. This gives us four types of dilemma.
§782.
(i). Simple Constructive.
If A is B or C is D, E is F.
Either A is B or C is D.
. • . E is F.
(2). Simple Destructive.
If A is B, C is D and E is F.
Either C is not D or E is not F.
. • . A is not B.
(3). Complex Constructive.
If A is B, C is D ; and if E is F, G is H.
Either A is B or E is F.
. • . Either C is D or G is H.
2/0 OF THE MIXED FORM
(4). Complex Destructive.
If A is B, C is D ; and if E is F, G is H.
Either C is not D or G is not H.
. • . Either A is not B or E is not F.
§783.
(i). Simple Constructive.
If she sinks or if she swims, there will be an end
of her.
She must either sink or swim.
. • . There will be an end of her.
(2). Simple Destructive.
If I go to Town, I must pay for my ticket and pay
my hotel bill.
Either I cannot pay for my ticket or I cannot pay
my hotel bill.
. • . I cannot go to Town.
(3). Complex Constructive.
If I stay in this room, I shall be burnt to death,
and if I jump out of the window, I shall break
my neck.
I must either stay in the room or jump out of the
window.
. • . I must either be burnt to death or break my neck.
(4). Complex Destructive.
If he were clever, he would see his mistake ; and
if he were candid, he would acknowledge it.
OF COMPLEX SYLLOGISM. 271
Either he does not see his mistake or he will not
acknowledge it.
. • . Either he is not clever or he is not candid.
§ 784. It must be noticed that the simple destructive
dilemma would not admit of a disjunctive consequent. If
we said,
If A is B, either C is D or E is F,
Either C is not D or E is not F,
we should not be denying the consequent. For ' E is
not F ' would make it true that C is D, and ' C is not D '
would make it true that E is F ; so that in either case we
should have one of the alternatives true, which is just what
the disjunctive form ' Either C is D or E is F ' insists
upon.
§ 785. In the case of the complex constructive dilemma
the several members, instead of being distributively assigned
to one another, may be connected together as a whole —
thus—
If either A is B or E is F, either C is D or
GisH.
Either A is B or E is F.
. • . Either C is D or G is H.
In this shape the likeness of the dilemma to the partly
conjunctive syllogism is more immediately recognisable.
The major premiss in this shape is vaguer than in the
former. For each antecedent has now a disjunctive choice
of consequents, instead of being limited to one. This
vagueness, however, does not affect the conclusion. For,
so long as the conclusion is established, it does not matter
272 OF THE MIXED FORM
from which members of the major its own members
flow.
§ 786. It must be carefully noticed that we cannot treat
the complex destructive dilemma in the same way.
If either A is B or E is F, either C is D or
G is H.
Either C is not D or G is not H.
Since the consequents are no longer connected individu
ally with the antecedents, a disjunctive denial of them
leaves it still possible for the antecedent as a whole to be
true. For ' C is not D ' makes it true that G is H, and
' G is not H ' makes it true that C is D. In either case
then one is true, which is all that was demanded by the
consequent of the major. Hence the consequent has not
really been denied.
§ 787. For the sake of simplicity we have limited the
examples to the case of two antecedents or consequents.
But we may have as many of either as we please, so as to
have a Trilemma, a Tetralemma, and so on.
TRILEMMA.
If A is B, C is D ; and if E is F, G is H ; and if
K is L, M is N.
Either A is B or E is F or K is L.
. • . Either C is D or G is H or K is L.
§ 788. Having seen what the true dilemma is, we shall
now examine some forms of reasoning which resemble
dilemmas without being so.
OF COMPLEX SYLLOGISM. 373
§ 789. This, for instance, is not a dilemma —
If A is B orifE is F, C is D.
But A is B and E is F.
".-•. CisD.
If he observes the sabbath or if he refuses to eat
pork, he is a Jew.
But he both observes the sabbath and refuses to
eat pork.
. • . He is a Jew.
What we have here is a combination of two partly
conjunctive syllogisms with the same conclusion, which
would have been established by either of them singly.
The proof is redundant.
§ 790. Neither is the following a dilemma —
If A is B, C is D and E is F.
Neither C is D nor E is F.
, • . A is not B.
If this triangle is equilateral, its sides and its
angles will be equal.
But neither its sides nor its angles are equal.
. • . It is not equilateral.
This is another combination of two conjunctive syllo
gisms, both pointing to the same conclusion. The proof
is again redundant. In this case we have the consequent
denied in both, whereas in the former we had the antece
dent affirmed. It is only for convenience that such
arguments as these are thrown into the form of a single
T
274 OF THE MIXED FORM
syllogism. Their real distinctness may be seen from the
fact that we here deny each proposition separately, thus
making two independent statements — C is not D and E is
not F. But in the true instance of the simple destructive
dilemma, what we deny is not the truth of the two pro
positions contained in the consequent, but their compati
bility ; in other words we make a disjunctive denial.
§ 791. Nor yet is the following a dilemma —
If A is B, either C is D or E is F.
Neither C is D nor E is F.
. • . A is not B.
If the barometer falls there will be either wind or
rain.
There is neither wind nor rain.
. • . The barometer has not fallen.
What we have here is simply a conjunctive major with
the consequent denied in the minor. In the consequent
of the major it is asserted that the two propositions, ' C is
D ' and * E is F ' cannot both be false ; and in the minor
this is denied by the assertion that they are both false.
§ 792. A dilemma is said to be rebutted or retorted,
when another dilemma is made out proving an opposite
conclusion. If the dilemma be a sound one, and its
premisses true, this is of course impossible, and any
appearance of contradiction that may present itself on first
sight must vanish on inspection. The most usual mode
OF COMPLEX SYLLOGISM.
of rebutting a dilemma is by transposing and denying the
consequents in the major —
If A is B, C is D ; and if E is F, G is H.
Either A is B or E is F.
. • . Either C is D or G is H.
The same rebutted —
If A is B, G is not H ; and if E is F, C is not D.
Either A is B or E is F.
. • . Either G is not H or C is not D.
' . = Either C is not D or G is not H.
§ 793. Under this form comes the dilemma ad
dressed by the Athenian mother to her son — ' Do not
enter public life : for, if you say what is just, men will
hate you ; and, if you say what is unjust, the gods will
hate you/ to which the following retort was made— ' I
ought to enter public life : for, if I say what is just, the
gods will love me ; and, if I say what is unjust, men will
love me.' But the two conclusions here are quite com
patible. A man must, on the given premisses, be both
hated and loved, whatever course he takes. So far indeed
are two propositions of the form
Either C is D or G is H,
and Either C is not D or G is not H,
from being incompatible, that they express precisely the
same thing when contradictory alternatives have been
selected, e. g. —
Either a triangle is equilateral or non-equilateral.
Either a triangle is non-equilateral or equilateral.
T 2
276 OF THE MIXED FORM
§ 794. Equally illusory is the famous instance of re
butting a dilemma contained in the story of Protagoras
and Euathlus (Aul. Cell. Noct. Att. v. 10). Euathlus was
a pupil of Protagoras in rhetoric. He paid half the fee
demanded by his preceptor before receiving lessons, and
agreed to pay the remainder when he won his first case.
But as he never proceeded to practise at the bar, it
became evident that he meant to bilk his tutor. Accord
ingly Protagoras himself instituted a law-suit against him,
and in the preliminary proceedings before the jurors pro
pounded to him the following dilemma — ' Most foolish
young man, whatever be the issue of this suit, you must
pay me what I claim : for, if the verdict be given in your
favour, you are bound by our bargain ; and if it be given
against you, you are bound by the decision of the jurors.'
The pupil, however, was equal to the occasion, and re
butted the dilemma as follows — ' Most sapient master,
whatever be the issue of this suit, I shall not pay you
what you claim : for, if the verdict be given in my favour,
I am absolved by the decision of the jurors ; and, if it be
given against me, I am absolved by our bargain/ The
jurors are said to have been so puzzled by the conflicting
plausibility of the arguments that they adjourned the case
till the Greek Kalends. It is evident, however, that a
grave injustice was thus done to Protagoras. His dilemma
was really invincible. In the counter-dilemma of Euathlus
we are meant to infer that Protagoras would actually lose
his fee, instead of merely getting it in one way rather than
another. In either case he would both get and lose his
OF COMPLEX SYLLOGISM.
fee, in the sense of getting it on one plea, and not getting
it on another: but in neither case would he actually
lose it.
§ 795. If a dilemma is correct in form, the conclusion
of course rigorously follows : but a material fallacy often
underlies this form of argument in the tacit assumption
that the alternatives offered in the minor constitute an ex
haustive division. Thus the dilemma ' If pain is severe,
it will be brief; and if it last long it will be slight/ &c.,
leaves out of sight the unfortunate fact that pain may both
be severe and of long continuance. Again the following
dilemma —
If students are idle, examinations are unavailing ; and, if
they are industrious, examinations are superfluous,
Students are either idle or industrious,
. • . Examinations are either unavailing or superfluous,
is valid enough, so far as the form is concerned. But the
person who used it would doubtless mean to imply that
students could be exhaustively divided into the idle and
the industrious. No deductive conclusion can go further
than its premisses ; so that all that the above conclusion
can in strictness be taken to mean is that examinations are
unavailing, when students are idle, and superfluous, when
they are industrious — which is simply a reassertion as a
matter of fact of what was previously given as a pure
hypothesis.
CHAPTER XXVII.
Of the Reduction of the Dilemma.
§ 796. As the dilemma is only a peculiar variety of the
partly conjunctive syllogism, we should naturally expect
to find it reducible in the same way to the form of a
simple syllogism. And such is in fact the case. The
constructive dilemma conforms to the first figure and the
destructive to the second.
( L ) Simple Constructive Dilemma
If A is B or if E is F, C is D.)
Either A is B or E is F.
. • . C is D.
(2) Simple Destructive.
If A is B, C is D and E is F.}
Either C is not D or E is not F.
. • . A is not B.
Barbara.
All cases of either A being B or E
being F are cases of C being D.
All actual cases are cases of either
A being B or E being F.
All actual cases are cases of C
being D.
Camestres.
All cases of A being B are cases of
C being D and E being F.
No actual cases are cases of C being
D and E being F.
No actual cases are cases of A
being B.
OF THE REDUCTION OF THE DILEMMA.
179
(3) Complex Constructive.
If AisB,CisD; andifEisF,\
Gis H.
Either A is B or E is F.
, • . Either C is D or G is H.
(4) Complex Destructive.
If A is B, C is D ; and if E is F,
GisH.
Either C is not D or G is
not H.
• . Either A is not B or E is
not F.
Barbara.
All cases of either A being B or E
being F are cases of either C being
D or G being H.
All actual cases are cases of either A
being B or E being F.
All actual cases are cases of either C
being D or G being H.
All cases of A being B and E being F
are cases of C being D and G
being H.
No actual cases are cases of C being
D and G being H.
No actual cases are cases of A being
B and E being F.
§ 797. There is nothing to prevent our having Darii,
instead of Barbara, in the constructive form, and Baroko,
instead of Camestres, in the destructive. As in the case
of the partly conjunctive syllogism the remaining moods
of the first and second figure are obtained by taking a
negative proposition as the consequent of the major pre
miss, e.g. —
Simple Constructive.
If A is B or if E is F, C is not D- \
Either A is B or E is F.
. • . C is not D.
Celarent or Ferio.
No cases of either A being B or E
being F are cases of C being D.
All (or some) actual cases are cases of
either A being B or E being F.
All (or some) actual cases are not
cases of C being D.
CHAPTER XXVIII.
Of the Dilemma regarded as ' an Immediate
Inference.
§ 798. LIKE the partly conjunctive syllogism, the dilemma
can be expressed under the forms of immediate inference.
As before, the conclusion in the constructive type resolves
itself into the subalternate of the major itself, and in the
destructive type into the subalternate of its contrapositive.
The simple constructive dilemma, for instance, may be
read as follows —
If either A is B or E is F, C is D,
. • . Either A being B or E being F, C is D,
which is equivalent to
Every case of either A being B or E being F is a
case of C being D.
. • . Some case of either A being B or E being F is a
case of C being D.
The descent here from ' every ' to ' some ' takes the place
of the transition from hypothesis to fact.
DILEMMA AS IMMEDIATE INFERENCE. 281
§ 799. Again the complex destructive may be read
thus—
If A is B, C is D ; and if E is F, G is H,
. • . It not being true that C is D and G is H, it is not
true that A is B and E is F,
which may be resolved into two steps of immediate infer
ence, namely, conversion by contraposition followed by
subalternation —
All cases of A being B and E being F are cases of
C being D and G being H.
. • . Whatever is not a case of C being D and G being
H is not a case of A being B and E being F.
. • . Some case which is not one of C being D and G
being H is not a case of A being B and E
being F.
CHAPTER XXIX.
Of Trains of Reasoning.
§ 800. THE formal logician is only concerned to examine
whether the conclusion duly follows from the premisses :
he need not concern himself with the truth or falsity of his
data. But the premisses of one syllogism may themselves
be conclusions deduced from other syllogisms, the
premisses of which may in their turn have been estab
lished by yet earlier syllogisms. When syllogisms are
thus linked together we have what is called a Train of
Reasoning.
§ 801. It is plain that all truths cannot be established
by reasoning. For the attempt to do so would involve
us in an infinite regress, wherein the number of syllogisms
required would increase at each step in a geometrical
ratio. To establish the premisses of a given syllogism we
should require two preceding syllogisms ; to establish
their premisses, four ; at the next step backwards, eight ;
at the next, sixteen ; and so on ad infinitum. Thus the
very possibility of reasoning implies truths that are known
to us prior to all reasoning ; and, however long a train of
reasoning may be, we must ultimately come to truths
which are either self-evident or are taken for granted.
§ 802. Any syllogism which establishes one of the
premisses of another is called in reference to that other a
OF TRAINS OF REASONING. 283
Pro- syllogism, while a syllogism which has for one of its
premisses the conclusion of another syllogism is called in
reference to that other an Epi-syllogism.
The Epicheirema.
§ 803. The name Epicheirema is given to a syllogism
with one or both of its premisses supported by a reason.
Thus the following is a double epicheirema —
All B is A, for it is E.
All C is B, for it is F.
.• . A11C is A.
All virtue is praiseworthy, for it promotes the general
welfare.
Generosity is a virtue, for it prompts men to postpone
self to others.
. • . Generosity is praiseworthy.
§ 804. An epicheirema is said to be of the first or
second order according as the major or minor premiss is
thus supported. The double epicheirema is a combina
tion of the two orders.
§ 805. An epicheirema, it will be seen, consists of one
syllogism fully expressed together with one, or, it may be,
two enthymemes (§ 557). In the above instance, if the
reasoning which supports the premisses were set forth at
full length, we should have, in place of the enthymemes,
the two following pro-syllogisms —
(i) All E is A.
All B is E.
. • . All B is A.
284 OF TRAINS OF REASONING.
Whatever promotes the general welfare is praise
worthy.
Every virtue promotes the general welfare.
. • . Every virtue is praiseworthy.
(2) All F is B.
All C is F.
. • . All C is B.
Whatever prompts men to postpone self to others is
a virtue.
Generosity prompts men to postpone self to others.
. • . Generosity is a virtue.
§ 806. The enthymemes in the instance above given are
both of the first order, having the major premiss suppressed.
But there is nothing to prevent one or both of them from
being of the second order —
All B is A, because all F is.
All C is B, because all F is.
. • . All C is A.
All Mahometans are fanatics, because all Monotheists
are.
These men are Mahometans, because all Persians are.
. • . These men are fanatics.
Here it is the minor premiss in each syllogism that is
suppressed, namely,
(1) All Mahometans are Monotheists.
(2) These men are Persians.
OF TRAINS OF REASONING. 285
The Sorites.
§ 807. The Sorites is the neatest and most compendious
form that can be assumed by a train of reasoning.
§ 808. It is sometimes more appropriately called the
chain-argument, and may be defined as —
A train of reasoning, in which one premiss of each
epi-syllogism is supported by a pro-syllogism, the other
being taken for granted.
This is its inner essence.
§ 809. In its outward form it may be described as — A
series of propositions, each of which has one term in
common with that which preceded it, while in the con
clusion one of the terms in the last proposition becomes
either subject or predicate to one of the terms in the first.
§ 810. A sorites may be either —
(i) Progressive,
or (2) Regressive.
Progressive Sorites. Regressive Sorites.
All A is B. All D is E.
. All B is C. All C is D,
All C is D. All B is C.
All D is E. All A is B.
. • . All A is E. . • . All A is E.
§ 811. The usual form is the progressive; so that the
sorites is commonly described as a series of propositions
in which the predicate of each becomes the subject of the
next, while in the conclusion the last predicate is afiirmed
286 OF TRAINS OF REASONING.
or denied of the first subject. The regressive form,
however, exactly reverses these attributes ; and would
require to be described as a series of propositions, in
which the subject of each becomes the predicate of the
next, while in the conclusion the first predicate is affirmed
or denied of the last subject.
§ 812. The regressive sorites, it will be observed, con
sists of the same propositions as the progressive one, only
written in reverse order. Why then, it may be asked, do
we give a special name to it, though we do not consider a
syllogism different, if the minor premiss happens to precede
the major ? It is because the sorites is not a mere series
of propositions, but a compressed train of reasoning ; and
the two trains of reasoning may be resolved into their
component syllogisms in such a manner as to exhibit a
real difference between them.
§ 813. The Progressive Sorites is a train of reasoning in
which the minor premiss of each epi-syllogism is supported
by a pro-syllogism, while the major is taken for granted.
§ 814. The Regressive Sorites is a train of reasoning
in which the major premiss of each epi-syllogism is sup
ported by a pro-syllogism, while the minor is taken for
granted.
Progressive Sorites. Regressive Sorites.
(i) AllBisC. (i) AllDisE.
All A is B. All C is D.
. • . All A is C. . • . All C is E.
OF TRAINS OF REASONING. 287
(2) All C is D. (2) All C is E.
All A is C. All B is C.
. • . All A is D. ., • . All B is E.
(3) All D is E. (3) All B is E.
All A is D. All A is B.
. • . All A is E. . • . All A is E.
§ 815. Here is a concrete example of the two kinds of
sorites, resolved each into its component syllogisms —
Progressive Sorites.
All Bideford men are Devonshire men.
All Devonshire men are Englishmen.
All Englishmen are Teutons.
All Teutons are Aryans.
. • . All Bideford men are Aryans.
(1) All Devonshire men are Englishmen.
All Bideford men are Devonshire men.
. * . All Bideford men are Englishmen.
(2) All Englishmen are Teutons.
All Bideford men are Englishmen.
. • . All Bideford men are Teutons.
(3) All Teutons are Aryans.
All Bideford men are Teutons.
. • . All Bideford men are Aryans.
288 OF TRAINS OF REASONING.
Regressive Sorites.
All Teutons are Aryans.
All Englishmen are Teutons.
All Devonshiremen are Englishmen.
All Bideford men are Devonshiremen.
. • . All Bideford men are Aryans.
(1) All Teutons are Aryans.
All Englishmen are Teutons.
. • . All Englishmen are Aryans.
(2) All Englishmen are Aryans.
All Devonshiremen are Englishmen.
. • . All Devonshiremen are Aryans.
(3) All Devonshiremen are Aryans.
All Bideford men are Devonshiremen.
. • . All Bideford men are Aryans.
§ 816. When expanded, the sorites is found to contain
as many syllogisms as there are propositions intermediate
between the first and the last. This is evident also on
inspection by counting the number of middle terms.
§ 817. In expanding the progressive form we have to
commence with the second proposition of the sorites
as the major premiss of the first syllogism. In the pro
gressive form the subject of the conclusion is the same in
all the syllogisms ; in the regressive form the predicate is
the same. In both the same series of means, or middle
OF TRAINS OF REASONING.
289
terms, is employed, the difference lying in the extremes
that are compared with one another through them.
§ 818. It is apparent from the figure that in the pro
gressive form we work from within outwards, in the
regressive form from without inwards. In the former we
first employ the term ' Devonshiremen ' as a mean to con
nect ' Bideford men ' with ' Englishmen ' ; next we employ
'Englishmen' as a mean to connect the same subject
'Bideford men' with the wider term 'Teutons'; and,
lastly, we employ ' Teutons ' as a mean to connect the
original subject 'Bideford men' with the ultimate predi
cate 'Ayrans.'
§ 819. Reversely, in the regressive form we first use
'Teutons' as a mean whereby to bring 'Englishmen'
under ' Aryans ' ; next we use ' Englishmen ' as a mean
whereby to bring ' Devonshiremen ' under the same predi
cate ' Aryans ' ; and, lastly, we use ' Devonshiremen ' as a
u
290 OF TRAINS OF REASONING.
mean whereby to bring the ultimate subject 'Bideford
men' under the original predicate 'Aryans/
§ 820. A sorites may be either Regular or Irregular.
§ 821. In the regular form the terms which connect
each proposition in the series with its predecessor, that is
to say, the middle terms, maintain a fixed relative position ;
so that, if the middle term be subject in one, it will
always be predicate in the other, and vice versa. In the
irregular form this symmetrical arrangement is violated.
§ 822. The syllogisms which compose a regular sorites,
whether progressive or regressive, will always be in the
first figure.
In the irregular sorites the syllogisms may fall into
different figures.
§ 823. For the regular sorites the following rules may
be laid down.
(1) Only one premiss can be particular, namely, the
first, if the sorites be progressive, the last, if it
be regressive.
(2) Only one premiss can be negative, namely, the
last, if the sorites be progressive, the first, if it
be regressive.
§ 824. Proof of the Rules for the Regular Sorites.
(i) In the progressive sorites the proposition which
stands first is the only one which appears as a
minor premiss in the expanded form. Each
of the others is used in its turn as a major.
If any proposition, therefore, but the first were
OF TRAINS OF REASONING. 291
particular, there would be a particular major,
which involves undistributed middle, if the
minor be affirmative, as it must be in the first
figure.
In the regressive sorites, if any proposition
except the last were particular, we should have
a particular conclusion in the syllogism in
which it occurred as a premiss, and so a par
ticular major in the next syllogism, which
again is inadmissible, as involving undistributed
middle.
(2) In the progressive sorites, if any premiss before
the last were negative, we should have a
negative conclusion in the syllogism in which
it occurs. This would necessitate a negative
minor in the next syllogism, which is inad
missible in the first figure, as involving illicit
process of the major.
In the regressive sorites the proposition
which stands first is the only one which ap
pears as a major premiss in the expanded form.
Each of the others is used in its turn as a
minor. If any premiss, therefore, but the first
were negative, we should have a negative minor
in the first figure, which involves illicit process
of the major.
§ 825. The rules above given do not apply to the
irregular sorites, except so far as that only one premiss
can be particular and only one negative, which follows
u 2
292
OF TRAINS OF REASONING.
from the general rules of syllogism. But there is nothing
to prevent any one premiss from being particular or any
one premiss from being negative, as the subjoined ex
amples will show. Both the instances chosen belong to
the progressive order of sorites.
All B is A.
All C is B.
Some C is D.
All D is E.
Some A is E.
All A is B.
All B is C.
No D is C.
All E is D.
No A is E.
(3)
Barbara.
All B is A.
All C is B.
All C is A.
Disamis.
Some C is D.
All C is A.
Some A is D.
Darii.
All D is E.
Some A is D.
Some A is E.
Barbara.
All B is C.
All A is B.
. All A is C.
Of TRAINS OF REASONING.
(2) Cesar e.
No D is C.
All A is C.
. • . No A is D.
(3) . Camestres.
All E is D.
No A is D.
. • . No A is E.
§ 826. A chain argument may be composed consisting
of conjunctive instead of simple propositions. This is
subject to the same laws as the simple sorites, to which
it is immediately reducible.
Progressive.
If A is B, C is D.
If C is D, E is F.
IfEisF, GisH.
If A is B, G is H.
Regressive.
If E is F, G is H.
If C is D, E is F.
If A is B, C is D.
If A is B, G is H,
CHAPTER XXX.
Of Fallacies.
§ 827. AFTER examining the conditions on which correct
thoughts depend, it is expedient to classify some of the
most familiar forms of error. It is by the treatment of the
Fallacies that logic chiefly vindicates its claim to be
considered a practical rather than a speculative science.
To explain and give a name to fallacies is like setting up
so many sign-posts on the various turns which it is
possible to take off the road of truth.
§ 828. By a fallacy is meant a piece of reasoning which
appears to establish a conclusion without really doing so.
The term applies both to the legitimate deduction of a
conclusion from false premisses and to the illegitimate
deduction of a conclusion from any premisses. There
are errors incidental to conception and judgement, which
might well be brought under the name ; but the fallacies
with which we shall concern ourselves are confined to
errors connected with inference.
OF FALLACIES. 295
§ 829. When any inference leads to a false conclusion,
the error may have arisen either in the thought itself or in
the signs by which the thought is conveyed. The main
sources of fallacy then are confined to two —
(1) thought,
(2) language.
§ 830. This is the basis of Aristotle's division of falla
cies, which has not yet been superseded. Fallacies,
according to him, are either in the language or outside of
it. Outside of language there is no source of error but
thought. For things themselves do not deceive us, but
error arises owing to a misinterpretation of things by the
mind. Thought, however, may err either in its form or in
its matter. The former is the case where there is some
violation of the laws of thought; the latter whenever
thought disagrees with its object. Hence we arrive at the
important distinction between Formal and Material falla
cies, both of which, however, fall under the same negative
head of fallacies other than those of language.
(In the language
(in the signs of thought)
/ In the Form.
Outside the language
(in the thought itself) 1
lln the Matter.
§ 831. There are then three heads to which fallacies
may be referred — namely, Formal Fallacies, Fallacies of
296 OF FALLACIES.
Language, which are commonly known as Fallacies of
Ambiguity, and, lastly, Material Fallacies.
§ 832. Aristotle himself only goes so far as the first step
in the division of fallacies, being content to class them
according as they are in the language or outside of it.
After that he proceeds at once to enumerate the infimae
species under each of the two main heads. We shall
presently imitate this procedure for reasons of expediency.
For the whole phraseology of the subject is derived from
Aristotle's treatise on Sophistical Refutations, and we
must either keep to his method or break away from
tradition altogether. Sufficient confusion has already
arisen from retaining Aristotle's language while neglecting
his meaning.
§ 833. Modern writers on logic do not approach
fallacies from the same point of view as Aristotle. Their
object is to discover the most fertile sources of error in
solitary reasoning ; his was to enumerate the various
tricks of refutation which could be employed by a sophist
in controversy. Aristotle's classification is an appendix to
the Art of Dialectic.
§ 834. Another cause of confusion in this part of logic
is the identification of Aristotle's two-fold division of
fallacies, commonly known under the titles of In dictione
and Extra dictionem, with the division into Logical and
Material, which is based on quite a different principle.
§ 835. Aristotle's division perhaps allows an undue
importance to language, in making that the principle of
division, and so throwing formal and material fallacies
OF FALLACIES. 297
under a common head. Accordingly another classification
has been adopted, which concentrates attention from the
first upon the process of thought, which ought certainly
to be of primary importance in the eyes of the logician.
This classification is as follows.
§ 836. Whenever in the course of our reasoning we are
involved in error, either the conclusion follows from the
premisses or it does not. If it does not, the fault must lie
in the process of reasoning, and we have then what is
called a Logical Fallacy. If, on the other hand, the con
clusion does follow from the premisses, the fault must lie
in the premisses themselves, and we then have what is
called a Material Fallacy. Sometimes, however, the con
clusion will appear to follow from the premisses until the
meaning of the terms is examined, when it will be found
that the appearance is deceptive owing to some ambiguity
in the language. Such fallacies as these are, strictly
speaking, non-logical, since the meaning of words is ex
traneous to the science which deals with thought. But they
are called Semi-logical. Thus we arrive by a different road
at the same three heads as before, namely, (i) Formal or
Purely Logical Fallacies, (2) Semi-logical Fallacies or
Fallacies of Ambiguity, (3) Material Fallacies.
§ 837. For the sake of distinctness we will place the
two divisions side by side, before we proceed to enumerate
the infinite species.
298 OF FALLACIES.
In the language
(Fallacy of Ambiguity)
Fallacy .
(In the Form.
In the Matter.
Formal
or purely logical.
Logical \
Fallacy •(
(
Semi-logical
V (Fallacy of Ambiguity).
\Material
§ 838. Of one of these three heads, namely, formal
fallacies, it is not necessary to say much, as they have
been amply treated of in the preceding pages. A formal
fallacy arises from the breach of any of the general rules
of syllogism. Consequently it would be a formal fallacy
to present as a syllogism anything which had more or
less than two premisses. Under the latter variety comes
what is called ' a woman's reason/ which asserts upon its
own evidence something which requires to be proved.
Schoolboys also have been known to resort to this form
of argument — ' You're a fool.' ' Why ? ' ' Because you
are/ When the conclusion thus merely reasserts one of
the premisses, the other must be either absent or irrelevant.
If, on the other hand, there are more than two premisses,
either there is more than one syllogism or the superfluous
premiss is no premiss at all, but a proposition irrelevant
to the conclusion.
§ 839. The remaining rules of the syllogism are more
OF FALLACIES. 399
liable to be broken than the first ; so that the following
scheme presents the varieties of formal fallacy which are
commonly enumerated —
/Four Terms.
Undistributed Middle.
Formal Fallacy^
Illicit Process.
\Negative Premisses and Conclusion.
§ 840. The Fallacy of Four Terms is a violation of the
second of the general rules of syllogism (§ 582). Here
is a palpable instance of it —
All men who write books are authors.
All educated men could write books.
. • . All educated men are authors.
Here the middle term is altered in the minor premiss to
the destruction of the argument. The difference between
the actual writing of books and the power to write them
is precisely the difference between one who is an author
and one who is not.
§ 841. Since a syllogism consists of three terms, each
of which is used twice over, it would be possible to have
an apparent syllogism with as many as six terms in it.
The true name for the fallacy therefore is the Fallacy of
More than Three Terms. But it is rare to find an
attempted syllogism which has more than four terms in it,
just as we are seldom tendered a line as an hexameter,
which has more than seven feet.
§ 842. The Fallacies of Undistributed Middle and
Illicit Process have been treated of under §§ 585, 586.
300 OF FALLACIES.
The heading ' Negative Premisses and Conclusion '
covers violations of the three general rules of syllogism
relating to negative premisses (§§ 590-593). Here is an
instance of the particular form of the fallacy which consists
in the attempt to extract an affirmative conclusion out of
two negative premisses —
All salmon are fish, for neither salmon nor fish belong
to the class mammalia.
The accident of a conclusion being true often helps to
conceal the fact that it is illegitimately arrived at.
The formal fallacies which have just been enumerated
find no place in Aristotle's division. The reason is plain.
His object was to enumerate the various modes in which
a sophist might snatch an apparent victory, whereas by
openly violating any of the laws of syllogism a disputant
would be simply courting defeat.
§ 843. We now revert to Aristotle's classification of
fallacies, or rather of Modes of Refutation. We will take
the species he enumerates in their order, and notice how
modern usage has departed from the original meaning of
the terms. Let it be borne in mind that, when the decep
tion was not in the language, Aristotle did not trouble
himself to determine whether it lay in the matter or in
the form of thought.
§ 844. The following scheme presents the Aristotelian
classification to the eye at a glance : —
OF FALLACIES.
301
Modes of .
Refutation \
In the language
Outside the language *
Equivocation.
Amphiboly.
Composition.
Division.
Accent.
Figure of Speech.
f Accident.
A dicto secundum quid.
Ignoratio Elenchi.
Consequent.
Petitio Principii.
Non causa pro causa.
\Many Questions.
§ 845. The Fallacy of Equivocation (6/icoi/v/iia) consists
in an ambiguous use of any of the three terms of a
syllogism. If, for instance, anyone were to argue thus—
No human being is made of paper,
All pages are human beings,
. • . No pages are made of paper —
the conclusion would appear paradoxical, if the minor
term were there taken in a different sense from that which
it bore in its proper premiss. This therefore would be
an instance of the fallacy of Equivocal Minor.
§ 846. For a glaring instance of the fallacy of Equivocal
Major, we may take the following —
No courageous creature flies,
The eagle is a courageous creature,
. • . The eagle does not fly —
1 The Greek is irapa TT)J/ Ae£tp, the exact meaning of which is
' due to the statement.'
302 OF FALLACIES.
the conclusion here becomes unsound only by the major
being taken ambiguously.
§ 847. It is, however, to the middle term that an am
biguity most frequently attaches. In this case the fallacy
of equivocation assumes the special name of the Fallacy of
Ambiguous Middle. Take as an instance the following —
Faith is a moral virtue.
To believe in the Book of Mormon is faith.
. • . To believe in the Book of Mormon is a moral
virtue.
Here the premisses singly might be granted; but the
conclusion would probably be felt to be unsatisfactory.
Nor is the reason far to seek. It is evident that belief in
a book cannot be faith in any sense in which that quality
can rightly be pronounced to be a moral virtue.
§ 848. The Fallacy of Amphiboly (d/z(£t/3oXi'u) is an
ambiguity attaching to the construction of a proposition
rather than to the terms of which it is composed. One of
Aristotle's examples is this —
TO @ov\€ff$ai Xafiftv /Lie rovs TTO\€/MOVS,
which may be interpreted to mean either ' the fact of my
wishing to take the enemy/ or ' the fact of the enemies'
wishing to take me/ The classical languages are espe
cially liable to this fallacy owing to the oblique construc
tion in which the accusative becomes subject to the verb.
Thus in Latin we have the oracle given to Pyrrhus
OF FALLACIES. 303
(though of course, if delivered at all, it must have been in
Greek)—
Aio te, JEacida, Romanes vincere posse1.
Pyrrhus the Romans shall, I say, subdue (Whately),
which Pyrrhus, as the story runs, interpreted to mean
that he could conquer the Romans, whereas the oracle
subsequently explained to him that the real meaning was
that the Romans could conquer him. Similar to this, as
Shakspeare makes the Duke of York point out, is the
witch's prophecy in Henry VI (Second Part, Act i, sc. 4),
The duke yet lives that Henry shall depose.
An instance of amphiboly may be read on the walls of
Windsor Castle — Hoc fecit Wykeham. The king was
incensed with the bishop for daring to record that he
made the tower, but the latter adroitly replied that what
he really meant to indicate was that the tower was the
making of him. To the same head may be referred the
famous sentence — ' I will wear no clothes to distinguish
me from my Christian brethren.'
§ 849. The Fallacy of Composition (o-vvOeais) is like
wise a case of ambiguous construction. It consists, as
expounded by Aristotle, in taking words together which
ought to be taken separately, e. g.
' Is it possible for a man who is not writing to write ? '
' Of course it is/ ' Then it is possible for a man to write
without writing/
1 Cicero, De Divinatione, ii. § 116 ; Quintilian, Inst. Orat. vii 9.
§6.
304 OF FALLACIES.
And again —
' Can you carry this, that, and the other ? ' ' Yes.'
' Then you can carry this, that, and the other/ —
a fallacy against which horses would protest, if they could.
§ 850. It is doubtless this last example which has led
to a convenient misuse of the term ' fallacy of composition'
among modern writers, by whom it is defined to consist
in arguing from the distributive to the collective use of a
term.
§ 851. The Fallacy of Division (diaipeo-is), on the other
hand, consists in taking words separately which ought to
be taken together, e. g.
€70; a' eOrjKa 5ov\ov OVT' (\cv0fpov1,
where the separation of 8ov\ov from ovra would lead to an
interpretation exactly contrary to what is intended.
And again —
irevTrjKOVT' dvSpwv tKarbv \iire Sios 'AxiAAeus,
where the separation of dvdpS>v from CKCITOV leads to a
ludicrous error.
Any reader whose youth may have been nourished on
' The Fairchild Family ' may possibly recollect a sentence
which ran somewhat on this wise — ' Henry,' said Mr.
Fairchild, ' is this true ? Are you a thief and a liar too ? '
But I am afraid he will miss the keen delight which can
be extracted at a certain age from turning the tables upon
Mr. Fairchild thus — Henry said, ' Mr. Fairchild, is this
true ? AiQyou a thief and a liar too ? '
1 Evidently the original of the line in Terence's Andria, 37, —
fed ex servo ut esses libertus mihi.
OF FALLACIES. 305
§ 852. The fallacy of division has been accommodated
by modern writers to the meaning which they have assigned
to the fallacy of composition. So that by the ' fallacy of
division ' is now meant arguing from the collective to the
distributive use of a term. Further, it is laid down that
when the middle term is used distributively in the major
premiss and collectively in the minor, we have the fallacy
of composition ; whereas, when the middle term is used
collectively in the major premiss and distributively in the
minor, we have the fallacy of division. Thus the first of
the two examples appended would be composition and
the second division.
(1) Two and three are odd and even.
Five is two and three.
. • . Five is odd and even.
(2) The Germans are an intellectual people.
Hans and Fritz are Germans.
. • . They are intellectual people.
§ 853. As the possibility of this sort of ambiguity is not
confined to the middle term, it seems desirable to add that
when either the major or minor term is used distributively
in the premiss and collectively in the conclusion, we have
the fallacy of composition, and in the converse case the
fallacy of division. Here is an instance of the latter kind
in which the minor term is at fault —
Anything over a hundredweight is too heavy to lift.
These sacks (collectively) are over a hundredweight.
. • . These sacks (distributively) are too heavy to lift.
306 OF FALLACIES.
§ 854. The ambiguity of the word ' all/ which has
been before commented upon (§ 119), is a great assist
ance in the English language to the pair of fallacies just
spoken of.
§ 855. The Fallacy of Accent (n-poo-wdia) is neither more
nor less than a mistake in Greek accentuation. As an
instance Aristotle gives Iliad xxiii. 328, where the
ancient copies of Homer made nonsense of the words TO
fieV ov KarairvdfTai fyi/3p« by writing ov with the circumflex
in place of ov with the acute accent 1. Aristotle remarks
that the fallacy is one which cannot easily occur in verbal
argument, but rather in writing and poetry.
§ 856. Modern writers explain the fallacy of accent to
be the mistake of laying the stress upon the wrong part of
a sentence. Thus when the country parson reads out,
' Thou shalt not bear false witness against thy neighbour/
with a strong emphasis upon the word 'against/ his
ignorant audience leap to the conclusion that it is not
amiss to tell lies provided they be in favour of one's
neighbour.
§ 857. The Fallacy of Figure of Speech (TO o-^/ia T^s
Xe^ecos) results from any confusion of grammatical forms, as
between the different genders of nouns or the different
voices of verbs, or their use as transitive or intransitive,
e.g. vyiaiveiv has the same grammatical form as rcfuvu' or
€ti/5 but the former is intransitive, while the latter are
1 This goes to show that the ancient Greeks did not distinguish
in pronunciation between the rough and smooth breathing any more
than their modern representatives.
OF FALLACIES. 307
transitive. A sophism of this kind is put into the mouth
of Socrates by Aristophanes in the Clouds (670-80).
The philosopher is there represented as arguing that
KcipdoTros must be masculine because KXecowjuos is. On the
surface this is connected with language, but it is essentially
a fallacy of false analogy.
§ 858. To this head may be referred what is known as
the Fallacy of Paronymous Terms. This is a species of
equivocation which consists in slipping from the use of
one part of speech to that of another, which is derived
from the same source, but has a different meaning. Thus
this fallacy would be committed if, starting from the fact
that there is a certain probability that a hand at whist will
consist of thirteen trumps, one were to proceed to argue
that it was probable, or that he had proved it.
§ 859. We turn now to the tricks of refutation which
lie outside the language, whether the deception be due to
the assumption of a false premiss or to some unsoundness
in the reasoning.
§ 860. The first on the list is the Fallacy of Accident
(ro o-vppfprjKos). This fallacy consists in confounding an
essential with an accidental difference, which is not allow
able, since many things are the same in essence, while
they differ in accidents. Here is the sort of example that
Aristotle gives —
' Is Plato different from Socrates ? ' ' Yes/ ' Is
Socrates a man ? ' ' Yes. ' ' Then Plato is different from
man/
To this we answer — No : the difference of accidents
X 2
308 OF FALLACIES.
between Plato and Socrates does not go so deep as to
affect the underlying essence. To put the thing more
plainly, the fallacy lies in assuming that whatever is differ
ent from a given subject must be different from it in all
respects, so that it is impossible for them to have a com
mon predicate. Here Socrates and Plato, though different
from one another, are not so different but that they have
the common predicate f man.' The attempt to prove that
they have not involves an illicit process of the major.
§ 861. The next fallacy surfers from the want of a con
venient name. It is called by Aristotle ™ a.7r\<as rode 77 Trfj
X/yco-dat KOI pr) Kvpi<o$ Or, more briefly, TO dn\a>s T) fir], or TO
Try KOL d7r\S>s, and by the Latin writers 'Fallacia a dicto
secundum quid ad dictum simpliciter.5 It consists in
taking what is said in a particular respect as though it held
true without any restriction, e.g. that because the non
existent (TO w Sv) is a matter of opinion, that therefore the
non-existent is, or again that because the existent (TO 6V)
is not a man, that therefore the existent is not. Or again,
if an Indian, who as a whole is black, has white teeth, we
should be committing this species of fallacy in declaring
him to be both white and not-white. For he is only white
in a certain respect (7177), but not absolutely (drr\S)s).
More difficulty, says Aristotle, may arise when opposite
qualities exist in a thing in about an equal degree. When,
for instance, a thing is half white and half black, are we to
say that it is white or black ? This question the philoso
pher propounds, but does not answer. The force of it lies
in the implied attack on the Law of Contradiction. It
OF FALLACIES, 309
would seem in such a case that a thing may be both white
and not-white at the same time. The fact is — so subtle
are the ambiguities of language — that even such a question
as ' Is a thing white or not-white ? ' straightforward, as
it seems, is not really a fair one. We are entitled some
times to take the bull by the horns, and answer with the
adventurous interlocutor in one of Plato's dialogues —
' Both and neither.' It may be both in a certain respect,
and yet neither absolutely.
§ 862. The same sort of difficulties attach to the Law
of Excluded Middle, and may be met in the same way.
It might, for instance, be urged that it could not be said
with truth of the statue seen by Nebuchadnezzar in his
dream either that it was made of gold or that it was not
made of gold : but the apparent plausibility of the objec
tion would be due merely to the ambiguity of language.
It is not true, on the one hand, that it was made of gold
(in the sense of being composed entirely of that metal) ;
and it is not true, on the other, that it was not made of
gold (in the sense of no gold at all entering into its com
position). But let the ambiguous proposition be split up
into its two meanings, and the stringency of the Law of
Excluded Middle will at once appear —
(1) It must either have been composed entirely of
gold or not.
(2) Either gold must have entered into its composi
tion or not.
§ 863. By some writers this fallacy is treated as the
310 OF FALLACIES.
converse of the last, the fallacy of accident being assimi
lated to it under the title of the ' Fallacia a dicto simpliciter
ad dictum secundum quid.' In this sense the two fallacies
may be denned thus.
The Fallacy of Accident consists in assuming that what
holds true as a general rule will hold true under some
special circumstances which may entirely alter the case.
The Converse Fallacy of Accident consists in assuming
that what holds true under some special circumstances
must hold true as a general rule.
The man who, acting on the assumption that alcohol is
a poison, refuses to take it when he is ordered to do so by
the doctor, is guilty of the fallacy of accident ; the man
who, having had it prescribed for him when he was ill,
continues to take it morning, noon, and night, commits
the converse fallacy.
§ 864. There ought to be added a third head to cover
the fallacy of arguing from one special case to another.
§ 865. The next fallacy is Ignoratio Elenchi (A/ygov
ayvoia). This fallacy arises when by reasoning valid in
itself one establishes a conclusion other than what is
required to upset the adversary's assertion. It is due to
an inadequate conception of the true nature of refutation.
Aristotle therefore is at the pains to define refutation at
full length, thus —
'A refutation (eXryx°0 is the denial of one and the
same — not name, but thing, and by means, not of a
synonymous term, but of the same term, as a necessary
consequence from the data, without assumption of the
OF FALLACIES. 311
point originally at issue, in the same respect, and in the same
relation, and in the same way, and at the same time/
The elenchus then is the exact contradictory of the
opponent's assertion under the terms of the law of contra
diction. To establish by a syllogism, or series of
syllogisms, any other proposition, however slightly differ
ent, is to commit this fallacy. Even if the substance of
the contradiction be established, it is not enough unless
the identical words of the opponent are employed in the
contradictory. Thus if his thesis asserts or denies some
thing about XcoTrtov, it is not enough for you to prove the
contradictory with regard to ipariov. There will be need
of a further question and answer to identify the two,
though they are admittedly synonymous. Such was the
rigour with which the rules of the game of dialectic were
enforced among the Greeks !
§ 866. Under the head of Ignoratio Elenchi it has
become usual to speak of various forms of argument which
have been labelled by the Latin writers under such names
as ' argumentum ad hominem,' ' ad populum/ ' ad verecun-
diam/ -'ad ignorantiam/ 'ad baculum' — all of them
opposed to the ' argumentum ad rem ' or ' ad judicium.'
§ 867. By the * argumentum ad hominem ' was perhaps
meant a piece of reasoning which availed to silence a
particular person, without touching the truth of the question.
Thus a quotation from Scripture is sufficient to stop the
mouth of a believer in the inspiration of the Bible.
Hume's Essay on Miracles is a noteworthy instance of the
1 argumentum ad hominem ' in this sense of the term. He
312 OF FALLACIES.
insists strongly on the evidence for certain miracles which
he knew that the prejudices of his hearers would prevent
their ever accepting, and then asks triumphantly if these
miracles, which are declared to have taken place in an
enlightened age in the full glare of publicity, are palpably
imposture, what credence can be attached to accounts of
extraordinary occurrences of remote antiquity, and con
nected with an obscure corner of the globe ? The
1 argumentum ad judicium ' would take miracles as a whole,
and endeavour to sift the amount of truth which may lie
in the accounts we have of them in every age J.
§ 868. In ordinary discourse at the present day the
term ' argumentum ad hominem ' is used for the form of
irrelevancy which consists in attacking the character of the
opponent instead of combating his arguments, as illustrated
in the well-known instructions to a barrister — ' No case :
abuse the plaintiff's attorney/
§ 869. The 'argumentum ad populum' consists in an ap
peal to the passions of one's audience. An appeal to passion,
or to give it a less question-begging name, to feeling, is
not necessarily amiss. The heart of man is the instrument
upon which the rhetorician plays, and he has to answer for
the harmony or the discord that comes of his performance.
§ 870. The ' argumentum ad verecundiam ' is an appeal
to the feeling of reverence or shame. It is an argument
much used by the old to the young and by Conservatives
to Radicals.
1 On this subject see the author's Attempts at Truth (Triibner
& Co.), pp. 46-59.
OF FALLACIES. 313
§871. The 'argumentum ad ignorantiam ' consists
simply in trading on the ignorance of the person addressed,
so that it covers any kind of fallacy that is likely to prove
effective with the hearer.
§ 872. The * argumentum ad baculum' is unquestion
ably a form of irrelevancy. To knock a man down when
he differs from you in opinion may prove your strength,
but hardly your logic.
A sub-variety of this form of irrelevancy was exhibited
lately at a socialist lecture in Oxford, at which an under
graduate, unable or unwilling to meet the arguments of
the speaker, uncorked a bottle, which had the effect of
instantaneously dispersing the audience. This might be
set down as the ' argumentum ad nasum/
§ 873. We now come to the Fallacy of the Consequent,
a term which has been more hopelessly abused than any.
What Aristotle meant by it was simply the assertion of the
consequent in a conjunctive proposition, which amounts to
the same thing as the simple conversion of A (§ 489),
and is a fallacy of distribution. Aristotle's example is
this —
If it has rained, the ground is wet.
. • . If the ground is wet, it has rained.
This fallacy, he tells us, is often employed in rhetoric
in dealing with presumptive evidence. Thus a speaker,
wanting to prove that a man is an adulterer, will argue
that he is a showy dresser, and has been seen about at
nights. Both these things however may be the case, and
yet the charge not be true.
314 OF FALLACIES.
§ 874. The Fallacy of Petitio or Assumptio Principii
(TO tv apxo aiTcitrSai or \ap.ftdvfiv) to which we now come,
consists in an unfair assumption of the point at issue.
The word aireurQai in Aristotle's name for it points to the
Greek method of dialectic by means of question and
answer. This fact is rather disguised by the mysterious
phrase ' begging the question.' The fallacy would be
committed when you asked your opponent to grant,
overtly or covertly, the very proposition originally pro
pounded for discussion.
§ 875. As the question of the precise nature of this
fallacy is of some importance we will take the words of
Aristotle himself (Top. viii. 13. §§ 2, 3). 'People seem
to beg the question in five ways. First and most glar
ingly, when one takes for granted the very thing that has
to be proved. This by itself does not readily escape
detection, but in the case of " synonyms," that is, where
the name and the definition have the same meaning, it
does so more easily1. Secondly, when one assumes
universally that which has to be proved in particular, as,
if a man undertaking to prove that there is one science of
contraries, were to assume that there is one science of
opposites generally. For he seems to be taking for
1 Some light is thrown upon this obscure passage by a comparison
with Cat. I. § 3, where ' synonym ' is defined. To take the word
here in its later and modern sense affords an easy interpretation,
which is countenanced by Alexander Aphrodisiensis, but it is flat
against the usage of Aristotle, who elsewhere gives the name
' synonym,' not to two names for the same thing, but to two things
going under the same name. See Trendelenberg on the passage.
OF FALLACIES. 315
granted along with several other things what he ought to
have proved by itself. Thirdly, when one assumes the
particulars where the universal has to be proved ; for in
so doing a man is taking for granted separately what
he was bound to prove along with several other things.
Again, when one assumes the question at issue by splitting
it up, for instance, if, when the point to be proved is that
the art of medicine deals with health and disease, one
were to take each by itself for granted. Lastly, if one
were to take for granted one of a pair of necessary con
sequences, as that the side is incommensurable with the
diagonal, when it is required to prove that the diagonal
is incommensurable with the side.'
§ 876. To sum up briefly, we may beg the question in
five ways —
(1) By simply asking the opponent to grant the point
which requires to be proved ;
(2) by asking him to grant some more general truth
which involves it;
(3) by asking him to grant the particular truths which
it involves ;
(4) by asking him to grant the component parts of it
in detail ;
(5) by asking him to grant a necessary consequence
of it.
§ 877. The first of these five ways, namely, that of
begging the question straight off, lands us in the formal
fallacy already spoken of (§ 838), which violates the
31 6 OF FALLACIES.
first of the general rules of syllogism, inasmuch as a
conclusion is derived from a single premiss, to wit, itself.
§ 878. The second, strange to say, gives us a sound
syllogism in Barbara, a fact which countenances the
blasphemers of the syllogism in the charge they bring
against it of containing in itself a petitio principii. Cer
tainly Aristotle's expression might have been more
guarded. But it is clear that his quarrel is with the
matter, not with the form in such an argument. The
fallacy consists in assuming a proposition wThich the op
ponent would be entitled to deny. Elsewhere Aristotle
tells us that the fallacy arises when a truth not evident by
its own light is taken to be so l.
§ 879. The third gives us an inductio per enumera-
tionem simplicem, a mode of argument which would of
course be unfair as against an opponent who was denying
the universal.
§ 880. The fourth is a more prolix form of the first.
§ 881. The fifth rests on Immediate Inference by
Relation (§ 534).
§ 882. Under the head of petitio principii comes the
fallacy of Arguing in a Circle, which is incidental to a
train of reasoning. In its most compressed form it may
be represented thus —
(i) B is A. (2) C is A.
C is B. B is C.
. • . C is A. . • . B is A.
1 "Orav TO (JL^J 81' avrov yvojcrrov 8t' avrov TIS
TOT' alreiTai TO e£ «/>X*7?- Anal. Pr. II. 1 6. § I ad fin.
OF FALLACIES. 317
§ 883. The Fallacy of Non causa pro causa (TO
co? aiTiov) is another, the name of which has led to a
complete misinterpretation. It consists in importing a
contradiction into the discussion, and then fathering it on
the position controverted. Such arguments, says Aris
totle, often impose upon the users of them themselves.
The instance he gives is too recondite to be of general
interest.
§ 884. Lastly, the Fallacy of Many Questions (TO ra
8vo tpc^T^ara ev -rroiflv) is a deceptive form of interro
gation, when a single answer is demanded to what is not
really a single question. In dialectical discussions the
respondent was limited to a simple ' yes ' or ' no ' ; and in
this fallacy the question is so framed as that either answer
would seem to imply the acceptance of a proposition
which would be repudiated. The old stock instance will
do as well as another — ' Come now. sir, answer " yes "
or " no." Have you left off beating your mother yet ? '
Either answer leads to an apparent admission of impiety.
A late Senior Proctor once enraged a man at a fair
with this form of fallacy. The man was exhibiting a blue
horse ; and the distinguished stranger asked him — ' With
what did you paint your horse ? '
EXERCISES.
EXERCISES.
THESE exercises should be supplemented by direct
questions upon the text, which it is easy for the
student or the teacher to supply for himself.
PART I.
CHAPTER I.
Classify the following words according as they are cate-
gorematic, syncategorematic or acategorematic : —
come
peradventure
why
through
inordinately
pshaw
therefore
circumspect
puss
grand
inasmuch
stop
touch
sameness
back
cage
disconsolate
candle.
CHAPTER II.
Classify the following things according as they are sub
stances, qualities or relations : —
God likeness weight
blueness grass imposition
ocean introduction thinness
man air spirit
Socrates raillery heat
mortality plum fire.
322 EXERCISES.
CHAPTER III.
1. Give six instances each of— attribute, abstract, singular,
privative, equivocal and relative terms.
2. Select from the following list of words such as are
terms, and state whether they are (i) abstract or concrete,
(2) singular or common, (3) uni vocal or equivocal : —
van table however
enter decidedly tiresome
very butt Solomon
infection bluff Czar
short although Caesarism
distance elderly Nihilist.
3. Which of the following words are abstract terms ? —
quadruped event through
hate desirability thorough
fact expressly thoroughness
faction wish light
inconvenient will garden
inconvenience volition grind.
4. Refer the following terms to their proper place under
each of the divisions in the scheme : —
horse husband London
free lump empty
liberty rational capital
impotent reason Capitol
impetuosity irrationality grave
impulsive double calf.
5. Give six instances each of proper names and desig
nations.
6. Give six instances each of connotative and non-conno-
tative terms.
EXERCISES. 323
7. Give the extension and intension of —
sermon animal sky
clock square gold
sport fish element
bird student fluid
art river line
gas servant language.
CHAPTER IV.
Arrange the following terms in order of extension — car
nivorous, thing, matter, mammal, organism, vertebrate, cat,
substance, animal.
PART II.
CHAPTER I.
Give a name to each of the following sentences : —
(1) Oh, that I had wings like a dove !
(2) The more, the merrier.
(3) Come rest in this bosom, my own stricken deer.
(4) Is there balm in Gilead ?
(5) Hearts may be trumps.
CHAPTER II.
Analyse the following propositions into subject, copula
and predicate : —
(1) He being dead yet speaketh.
(2) There are foolish politicians.
(3) Little does he care.
(4) There is a land of pure delight.
Y 2
334 EXERCISES.
(5) All's well that ends well.
(6) Sweet is the breath of morn.
(7) Now it came to pass that the beggar died.
(8) Who runs may read.
(9) Great is Diana of the Ephesians.
(10) Such things are.
(n) Not more than others I deserve.
(12) The day will come when Ilium's towers shall
perish.
CHAPTER III.
1. Express in logical form, affixing the proper symbol : —
(1) Some swans are not white.
(2) All things are possible to them that believe.
(3) No politicians are unprincipled.
(4) Some stones float on water.
(5) The snow has melted.
(6) Eggs are edible.
(7) All kings are not wise.
(8) Moths are not butterflies.
(9) Some men are born great.
(10) Not all who are called are chosen,
(n) It is not good for man to be alone.
(12) Men of talents have been known to fail in life.
(13) 'Tis none but a madman would throw about fire.
(14) Every bullet does not kill.
(15) Amongst Unionists are Whigs.
(16) Not all truths are to be told.
(17) Not all your efforts can save him.
(18) The whale is a mammal.
(19) Cotton is grown in Cyprus.
(20) An honest man's the noblest work of God.
(21) No news is good news.
(22) No friends are like old friends.
EXERCISES. 325
(23) Only the ignorant affect to despise knowledge.
(24) All that trust in Him shall not be ashamed.
(25) All is not gold that glitters.
(26) The sun shines upon the evil and upon the good.
(27) Not to go on is to go back.
(28) The king, minister, and general are a pretty trio.
(29) Amongst dogs are hounds.
(30) A fool is not always wrong.
(31) Alexander was magnanimous.
(32) Food is necessary to life.
(33) There are three things to be considered.
(34) By penitence the Eternal's wrath's appeased.
(35) Money is the miser's end.
(36) Few men succeed in life.
(37) All is lost, save honour.
(38) It is mean to hit a man when he is down.
(39) Nothing but coolness could have saved him.
(40) Books are generally useful.
(41) He envies others' virtue who has none himself.
(42) Thankless are all such offices.
(43) Only doctors understand this subject.
(44) All her guesses but two were correct.
(45) All the men were twelve.
(46) Gossip is seldom charitable.
2. Give six examples of indefinite propositions, and then
quantify them according to their matter.
3. Compose three propositions of each of the following
kinds : —
(1) with common terms for subjects ;
(2) with abstract terms for subjects ;
(3) with singular terms for predicates ;
(4) with collective terms for predicates ;
(5) with attributives in their subjects ;
(6) with abstract terms for predicates.
326 EXERCISES.
CHAPTER IV.
1. Point out what terms are distributed or undistributed
in the following propositions : —
(1) The Chinese are industrious.
(2) The angle in a semi-circle is a right angle.
(3) Not one of the crew survived.
(4) The weather is sometimes not propitious.
The same exercise may be performed upon any of the pro
positions in the preceding list.
2. Prove that in a negative proposition the predicate must
be distributed.
CHAPTER V.
Affix its proper symbol to each of the following pro
positions : —
(1) No lover he who is not always fond.
(2) There are Irishmen and Irishmen.
(3") Men only disagree,
Of creatures rational.
(4) Some wise men are poor.
(5) No Popes are some fallible beings.
(6) Some step-mothers are not unjust.
(7) The most original of the Roman poets was Lucretius.
(8) Some of the immediate inferences are all the forms
of conversion.
CHAPTER VI.
1. Give six examples of terms standing one to another as
genus to species.
EXERCISES.
3*7
2. To which of the heads of predicables would you refer
the following statements ? And why ?
(1) A circle is the largest space that can be contained
by one line.
(2) All the angles of a square are right angles.
(3) Man alone among animals possesses the faculty of
laughter.
(4) Some fungi are poisonous.
(5) Most natives of Africa are negroes.
(6) All democracies are governments.
(7) Queen Anne is dead.
CHAPTER VII.
1. Define the following terms —
Sun inn-keeper tea-pot
hope anger virtue
bread diplomacy milk
man death
telescope mountain'
senate novel.
carpet
sincerity
poverty
2. Define the
Economy —
Commodity
wealth
money
interest
credit
following terms as used in Political
barter value
land price
labour rent
capital wages
demand profits.
3. Criticise the following as definitions —
(1) Noon is the time when the shadows of bodies are
shortest.
(2) Grammar is the science of language.
(3) Grammar is a branch of philology.
328 EXERCISES.
(4) Grammar is the art of speaking and writing a lan
guage with propriety.
(5) Virtue is acting virtuously.
(6) Virtue is that line of conduct which tends to produce
happiness.
(7) A dog is an animal of the canine species.
(8) Logic is the art of reasoning.
(9) Logic is the science of the investigation of truth by
means of evidence.
(10) Music is an expensive noise.
(11) The sun is the centre of the solar system.
(12) The sun is the brightest of those heavenly bodies
that move round the earth.
(13) Rust is the red desquamation of old iron.
(14) Caviare is a kind of food.
(15) Life is the opposite of death.
(16) Man is a featherless biped.
(17) Man is a rational biped.
(18) A gentleman is a person who has no visible means
of subsistence.
(19) Fame is a fancied life in others' breath.
(20) A fault is a quality productive of evil or incon
venience.
(21) An oligarchy is the supremacy of the rich in a
state.
(22) A citizen is one who is qualified to exercise deliber
ative and judicial functions.
(23) Length is that dimension of a solid which would be
measured by the longest line.
(24) An eccentricity is a peculiar idiosyncrasy.
(25) Deliberation is that species of investigation which is
concerned with matters of action.
(26) Memory is that which helps us to forget.
(27) Politeness is the oil that lubricates the wheels of
society.
EXERCISES. 329
(28) An acute-angled triangle is one which has an acute
angle.
(29) A cause is that without which something would not
be.
(30) A cause is the invariable antecedent of a phenomenon.
(31) Necessity is the mother of invention.
(32) Peace is the absence of war.
(33) A net is a collection of holes strung together.
(34) Prudence is the ballast of the moral vessel.
(35) A circle is a plane figure contained by one line.
(36) Superstition is a tendency to look for constancy
where constancy is not to be expected.
(37) Bread is the staff of life.
(38) An attributive is a term which cannot stand as a
subject.
(39) Life is bottled sunshine.
(40) Eloquence is the power of influencing the feelings by
speech or writing.
(41) A tombstone is a monument erected over a grave in
memory of the dead.
(42) Whiteness is the property or power of exciting the
sensation of white.
(43) Figure is the limit of a solid.
(44) An archdeacon is one who exercises archidiaconal
functions.
(45) Humour is thinking in jest while feeling in earnest.
CHAPTER VIII.
.. Divide the following terms —
Soldier end book
church good oration
apple cause school
ship government letter
vehicle science verse.
330 EXERCISES.
•2. Divide the following terms as used in Political
Economy —
Requisites of production, labour, consumption, stock,
wealth, capital.
3. Criticise the following as divisions —
(1) Great Britain into England, Scotland, Wales, and
Ireland.
(2) Pictures into sacred, historical, landscape, and mytho
logical.
(3) Vertebrate animals into quadrupeds, birds, fishes,
and reptiles.
(4) Plant into stem, root, and branches.
(5) Ship into frigate, brig, schooner, and merchant-man.
(6) Books into octavo, quarto, green, and blue.
(7) Figure into curvilinear and rectilinear.
(8) Ends into those which are ends only, means and
ends, and means only.
(9) Church into Gothic, episcopal, high, and low.
(10) Sciences into physical, moral, metaphysical, and
medical.
(11) Library into public and private.
(12) Horses into race-horses, hunters, hacks, thorough
breds, ponies, and mules.
4. Define and divide —
Meat, money, virtue, triangle;
and give, as far as possible, a property and accident of each.
EXERCISES. 331
PART III.
CHAPTERS I-III.
1. What kind of influence have we here ? —
The author of the Iliad was unacquainted with
writing.
Homer was the author of the Iliad.
/. Homer was unacquainted with writing.
2. Give the logical opposites of the following propositions —
(1) Knowledge is never useless.
(2) All Europeans are civilised.
(3) Some monks are not illiterate.
(4) Happy is the man that findeth wisdom.
(5) No material substances are devoid of weight.
(6) Every mistake is not culpable.
(7) Some Irishmen are phlegmatic.
3. Granting the truth of the following propositions, what
other propositions can be inferred by opposition to be true or
false ?
(1) Men of science are often mistaken.
(2) He can't be wrong, whose life is in the right.
(3) Sir Walter Scott was the author of Waverley.
(4) The soul that sinneth it shall die.
(5) All women are not vain.
4. Granting the falsity of the following propositions, what
other propositions can be inferred by opposition to be true or
false ?—
(1) Some men are not mortal.
(2) Air has no weight.
332 EXERCISES.
(3) All actors are improper characters.
(4) None but dead languages are worth studying.
(5) Some elements are compound.
CHAPTER IV.
1. Give, as far as possible, the logical converse of each of
the following propositions —
(1) Energy commands success.
(2) Mortals cannot be happy.
(3) There are mistakes which are criminal.
(4) All's well that ends well.
(5) Envious men are disliked.
(6) A term is a kind of word or collection of words.
(7) Some Frenchmen are not vivacious.
(8) All things in heaven and earth were hateful to him.
(9) The square of three is nine.
(10) All cannot receive this saying.
(11) P struck Q.
(12) Amas.
2. ' More things may be contained in my philosophy than
exist in heaven or earth : but the converse proposition is by
no means true.' Is the term converse here used in its logical
meaning ?
CHAPTER V.
Permute the following propositions —
(1) All just acts are expedient.
(2) No display of passion is politic.
(3) Some clever people are not prudent.
(4) Some philosophers have been slaves.
The same exercise may be performed upon any of the
propositions in the preceding lists.
EXERCISES. 333
CHAPTER VI.
1. Give the converse by negation of —
(1) All women are lovely.
(2) Some statesmen are not practical.
(3) All lawyers are honest.
(4) All doctors are skilful.
(5) Some men are not rational.
2. Give the contrapositive of —
(1) All solid substances are material.
(2) All the men who do not row play cricket.
(3) All impeccable beings are other than human.
(4) Some prejudiced persons are not dishonest.
3. Prove indirectly the truth of the contrapositive of
All A is B.
4. Criticise the following as immediate inferences —
(1) All wise men are modest.
/. No immodest men are wise.
(2) Some German students are not industrious.
.'. Some industrious students are not Germans.
(3) Absolute difference excludes all likeness.
.'. Any likeness is a proof of sameness.
(4) None but the brave deserve the fair.
.*. All brave men deserve the fair.
(5) All discontented men are unhappy.
.'. No contented men are unhappy.
(6) Books being a source of instruction, our knowledge
must come from our libraries.
(7) All Jews are Semitic.
/. Some non-Semitic people are not Jews.
334 EXERCISES.
5. Show by what kind of inference each of the subjoined
propositions follows from
All discontented men are unhappy.
(1) All happy men are contented.
(2) Some discontented men are unhappy.
(3) Some contented men are happy.
(4) Some unhappy men are not contented.
(5) No discontented men are happy.
(6) Some happy men are contented.
(7) Some contented men are not unhappy.
(8) Some unhappy men are discontented.
(9) No happy men are discontented.
(10) Some discontented men are not happy.
(11) Some happy men are not discontented.
(12) None but unhappy men are discontented.
From how many of these propositions can the original one
be derived ? And why not from all ?
CHAPTER VII.
What kind of inference have we here ? —
(1) None but the ignorant despise knowledge.
/. No wise man despises knowledge.
(2) A is superior to B.
.'. B is inferior to A.
CHAPTER VIII.
Fill up the following enthymemes, mentioning to which
order they belong, and state which of them are expressed in
problematic form—
(i) I am fond of music: for I always like a comic song.
EXERCISES. 335
(2) All men are born to suffering, and therefore you
must expect your share.
(3) Job must have committed some secret sins : for he
fell into dreadful misfortunes.
(4) Latin was the language of the Vestals, and therefore
no lady need be ashamed of speaking it.
(5) None but physicians came to the meeting. There
were therefore no nurses there.
(6) The human soul extends through the whole body,
for it is found in every member.
(7) No traitor can be trusted, and you are a traitor.
(8) Whatever has no parts does not perish by the disso
lution of its parts. Therefore the soul of man is
imperishable.
Is the suppressed premiss in any case disputable on material
grounds ?
CHAPTERS IX— XVIII.
I.
Refer the following arguments to their proper mood and
figure, or show what rules of syllogism they violate —
(1) No miser is a true friend, for he does not assist
his friend with his purse.
(2) Governments are good which promote prosperity.
The goverment of Burmah does not promote
prosperity.
/. It is not a good government.
(3) Land is not property.
Land produces barley.
.*. Beer is intoxicating.
(4) Nothing is property but that which is the product
of man's hand.
The horse is not the product of man's hand.
.'. The horse is not property.
336 EXERCISES.
(5) Some Europeans at least are not Aryans, because
the Finns are not.
(6) Saturn is visible from the earth, and the moon is
visible from the earth. Therefore the moon is
visible from Saturn.
(7) Some men of self-command are poor, and there
fore some noble characters are poor.
(8) Sparing the rod spoils the child : so John will turn
out very good, for his mother beats him every
day.
(9) Some effects of labour are not painful, since every
virtue is an effect of labour.
(10) The courageous are confident and the experienced
are confident. Therefore the experienced are
courageous.
(11) No tale-bearer is to be trusted, and therefore no
great talker is to be trusted, for all tale-bearers
are great talkers.
(12) Socrates was wise, and wise men alone are happy:
therefore Socrates was happy.
II.
1. From the major ' No matter thinks ' draw, by supplying
the minor, the following conclusions —
(1) Some part of man does not think.
(2) The soul of man is not matter.
(3) Some part of man is not matter.
(4) Some substance does not think.
Name the figured mood into which each syllogism falls.
2. Construct syllogisms in the following moods and figures,
EXERCISES. 337
stating whether they are valid or invalid, and giving your
reasons in each case —
AEE in the first figure ; EAO in the second ; IAI in the
third ; All in the fourth.
3. Prove that ' Brass is not a metal/ using as your middle
term ' compound body.'
4. Construct syllogisms to prove or disprove —
(1) Some taxes are necessary.
(2) No men are free.
(3) Laws are salutary.
5. Prove by a syllogism in Bokardo that ' Some Socialists
are not unselfish,' and reduce your syllogism directly and in
directly.
6. Prove the following propositions in the second figure,
and reduce the syllogisms you use to the first —
(1) All negroes are not averse to education.
(2) Only murderers should be hanged.
7. Prove in Baroko and also in Ferio that ' Some Irishmen
are not Celts.'
8. Construct in words the same syllogism in all the four
figures.
9. Invent instances to show that false premisses may give
true conclusions.
III.
1. What moods are peculiar to the first, second, and third
figures respectively ?
2. What moods are common to all the figures ?
3. Why can there be no subaltern moods in the third
figure ?
4. What is the only kind of conclusion that can be drawn
in all the figures ?
z
33 8 EXERCISES.
5. Show that IEO violates the special rules of all the
figures.
6. In what figures is AEE valid ?
7. Show that AEO is superfluous in any figure.
8. Prove that O cannot be a premiss in the first figure, nor
a minor premiss anywhere but in the second.
9. Show that in the first figure the conclusion must have
the quality of the major premiss and the quantity of the
minor.
10. Why do the premisses EA yield a universal conclusion
in the first two figures and only a particular one in the last
two?
11. Show that AAI is the only mood in the fourth figure in
which it is possible for the major term to be distributed in
the premiss and undistributed in the conclusion.
12. Why are the premisses of Fesapo and Fresison not
transposed in reduction like those of the other moods of the
fourth figure ?
IV.
1. Why is it sufficient to distribute the middle term once
only ?
2. Prove that from two affirmative premisses you cannot
get a negative conclusion.
3. Prove that there must be at least one more term dis
tributed in the premisses than in the conclusion.
4. Prove that the number of distributed terms in the pre
misses cannot exceed those in the conclusion by more than
two.
5. Prove that the number of undistributed terms in the
premisses cannot exceed those in the conclusion by more
than one.
6. Prove that wherever the minor premiss is negative, the
major must be universal.
EXERCISES. 339
7. Prove that wherever the minor term is distributed, the
major premiss must be universal.
8. If the middle term be twice distributed, what mood and
figure are possible ?
9. If the major term of a syllogism be the predicate of the
major premiss, what do we know about the minor premiss ?
10. When the middle term is distributed in both premisses,
what must be the quantity of the conclusion ?
11. Prove that if the conclusion be universal, the middle
term can only be distributed once in the premisses.
12. Show how it is sometimes possible to draw three
different conclusions from the same premisses.
CHAPTER XIX.
1. Convert the following propositions —
(1) If a man is wise, he is humble.
(2) Where there is sincerity there is no affectation.
(3) When night-dogs run, all sorts of deer are chased.
(4) The nearer the Church, the further from God.
(5) If there were no void, all would be solid.
(6) Not to go on is sometimes to go back.
2. Express in a single proposition —
If he was divine, he was not covetous ; and if he was
covetous, he was not divine.
3. Exhibit the exact logical relation to one another of the
following pairs of propositions —
(i) If the conclusion be false, the premisses are false.
If the conclusion be true, the premisses are not
necessarily true.
z 2
340 EXERCISES.
(2) If one premiss be negative, the conclusion must be
negative.
If the conclusion be negative, one of the premisses
must be negative.
(3) The truth of the universal involves the truth of the
particular.
The falsity of the particular involves the falsity of
the universal.
(4) From the truth of the particular no conclusion follows
as to the universal.
From the falsity of the universal no conclusion follows
as to the particular.
(5) If the conclusion in the fourth figure be negative, the
major premiss must be universal.
If the major premiss in the fourth figure be particular,
the conclusion must be affirmative.
(6) If both premisses be affirmative, the conclusion must
be affirmative.
If the conclusion be negative, one of the premisses
must be negative.
4. ' The Method of Agreement stands on the ground that
whatever circumstance can be eliminated is not connected
with the phenomenon by any law ; the Method of Difference
stands on the ground that whatever circumstance cannot be
eliminated is connected with the phenomenon by a law.' Do
these two principles imply one another ?
CHAPTERS XX— XXVIII.
1. Fill up the following enthymemes, and state the exact
nature of the resulting syllogism —
(i) If Livy is a faultless historian, we must believe all
that he tells us : but that it is impossible to do.
EXERCISES. 341
(2) If they stay abroad, the wife will die ; while the
husband's lungs will not stand the English
climate. It is to be feared therefore that one
must fall a victim.
(3) He is either very good, very bad, or commonplace.
But he is not very good.
(4) Either a slave is capable of virtue or he is not.
.'. Either he ought not to be a slave or he is not
a man.
(5) Does not his feebleness of character indicate either
a bad training or a natural imbecility ?
(6) Those who ask shan't have ; those who don't ask
don't want.
(7) If a man be mad, he deviates from the common
standard of intellect.
.'. If all men be alike mad, no one is mad.
(8) ' I cannot dig ; to beg I am ashamed.'
2. 'The infinite divisibility of space implies that of time.
If the latter therefore be impossible, the former must be
equally so.' Formulate this argument as an immediate in
ference.
3. Examine the following arguments —
(1) If we have a dusty spring, there is always a good
wheat harvest. We shall therefore have a poor
harvest this year, for the spring has not been
dusty.
(2) Virtues are either feelings, capacities, or states ;
and as they are neither feelings nor capacities,
they must be states.
(3) Everything must be either just or unjust.
Justice is a thing, and is not unjust.
/. Justice is just.
Similarly justice is holy.
342 EXERCISES.
But the virtues of knowledge, justice, courage, tem
perance, and holiness were declared to be different
from one another.
.*. Justice is unholy and holiness unjust.
CHAPTER XXIX.
Formulate the following trains of reasoning, resolve them
into their component parts, and point out any violations of
the rules of syllogism which they may contain —
(1) No Church Institutions are useful ; for they teach
religious matters, not business matters, which
latter are useful, being profitable.
(2) Mr. Darwin long ago taught us that the clover crop
is dependent on the number of maiden ladies in
the district. For the ladies keep cats, and the
cats destroy the field-mice, which prey on the
bees, which, in their turn, are all-important agents
in the fertilisation of the clover flowers.
(3) Athletic games are duties ; for whatever is neces
sary to health is a duty, and exercise is necessary
to health, and these games are exercise.
(4) The iron-trade leads to the improvement of a new
country ; for furnaces require to be fed with fuel,
which causes land to be cleared.
(5) ' Is stone a body?' ' Yes.' ' Well, is not an animal
a body ? ' ' Yes.' ' And are you an animal ? ' l It
seems so.' ' Then you are a stone, being an
animal.'
(6) If A is B, C is D.
If E is F, Gis H.
But if A is B, E is F.
.-. If C is D, G is sometimes H.
EXERCISES. 343
(7) The soul is not matter.
/. My arm is not myself.
(8) Honesty deserves reward and a negro is a fellow-
creature. Therefore an honest negro is a fellow-
creature deserving of reward.
CHAPTER XXX.
1. Point out any ambiguities which underlie the following
propositions —
(1) Every one who has read the book in French will
recommend those who have not to read it in
English.
(2) I will not do this because he did it.
(3) These are all my books.
(4) By an old statute of the date of Edward III it was
accorded ' that Parliament should be holden
every year once or more often if need be.'
(5) They found Mary and Joseph and the babe lying
in a manger.
(6) The king and his minister are feeble and un
scrupulous.
(7) Heres meus uxori meae triginta pondo vasorum
argenteorum dato, quae volet.
2. Examine the following arguments, formulating them
when sound, and referring them, when unsound, to the proper
head of fallacy—
(1) We know that thou art a teacher come from God ;
for no man can do these signs that thou doest,
except God be with him. S. John iii. 2.
(2) ' Sir Walter Scott's novels have ceased to be
popular.' 'Well, that's only because nobody
reads them.'
344 EXERCISES.
(3) What we produce is property.
The sheriff produces a prisoner.
.*. A prisoner is property.
(4) As all metals are not necessarily solid, we may
expect some metals to be liquid.
(5) Moses was the son of Pharaoh's daughter.
.*. Moses was the daughter of Pharaoh's son.
(6) If Aeschines took part in the public rejoicings over
the success of my policy, he is inconsistent in
condemning it now; if he did not, he was a
traitor then.
(7) It is wrong to stick knives into people.
.'. Surgeons ought to be punished.
(8) If a thing admits of being taught, there must be
both teachers and learners of it.
,'. If there are neither teachers nor learners of a thing,
that thing does not admit of being taught.
(9) It is unnecessary to lend books, if they are com
mon, and wrong to lend them, if they are rare.
Therefore books should not be lent from public
libraries.
(10) Seeing is believing.
/. What is not seen cannot be believed.
(11) St. Paul was not of Jewish blood, for he was a
Roman citizen.
(12) To call you an animal is to speak the truth.
To call you an ass is to call you an animal.
/. To call you an ass is to speak the truth.
(13) Pain chastens folly. A life of ease must therefore
be one of folly incurable.
(14) We cannot be happy in this world ; for we must
either indulge our passions or combat them.
EXERCISES. 345
(15) It must be clear to the most unlettered mind that,
as all things were originally created by the Deity,
including the hair on our heads and the beards on
our faces, there can be no such thing as property.
(16) The crime was committed by the criminal.
The criminal was committed by the magistrate.
/. The crime was committed by the magistrate.
(17) General councils are as likely to err as the fallible
men of whom they consist.
(18) Dead dogs are heavier than living ones, because
vitality is buoyant.
(19) Deliberation is concerned with actions.
Actions are means.
/, Deliberation is concerned with means.
(20) ' No beast so fierce but has a touch of pity ;
But I have none : therefore I am no beast.'
(21) Practical pursuits are better than theoretical.
.'. Mathematics are better than logic.
(22) Death must be a good. For either the soul, ceas
ing to be, ceases to suffer, or, continuing to be,
lives in a better state.
(23) What is right should be enforced by law.
.'. Charity should be so enforced.
(24) All animals were in the Ark.
/. No animals perished in the Flood.
(25) If he robs, he is not honourable.
If he pays all his dues, he does not rob.
/. If he pays all his dues, he is honourable.
(26) A dove can fly a mile in a minute.
A swallow can fly faster than a dove.
/. A swallow can fly more than a mile in a minute.
(27) ' I must soap myself, because it's Sunday.'
1 Then do you only soap yourself on Sunday ' ?
34-6 EXERCISES.
(28) If the charge is false, the author of it is either
ignorant or malicious. But the charge is true.
Therefore he is neither.
(29) All the angles of a triangle are equal to two right
angles.
The angle at the vertex is an angle of a triangle.
.'. It is equal to two right angles.
(3°) Si gravis sit dolor, brevis est ; si longus, levis.
Ergo fortiter ferendus.
(31) You are not what I am.
I am a man.
.'. You are not a man.
(32) The extension of the franchise is necessary, for it
is imperative that the right of voting should be
granted to classes who have hitherto not pos
sessed this privilege.
(33) If Hannibal is really victorious, he does not need
supplies ; while, if he is deluding us, we ought
certainly not to encourage him by sending them.
Livy, xxiii. 13. § 5.
(34) Laws must punish, and punishment hurts.
All laws therefore are hurtful.
(35) The sun is an insensible thing.
The Persians worship the sun.
/. The Persians worship an insensible thing.
(36) Some ores are not metals ; for they are not fluids,
and some metals are not fluids.
(37) All the Grecian soldiers put the Persians to flight.
.*. Every Grecian soldier could rout the Persians.
(38) The resurrection of Jesus Christ is either an isolated
fact or else admits of parallel. But if it be an
isolated fact, it cannot be rendered probable to
one who denies the authority of Christianity;
EXERCISES. 347
and, if it admit of parallel, it no longer proves
what is required. Therefore it is either incapable
of being substantiated or else makes nothing for
the truth of Christianity.
(39) The resurrection of Christ in the flesh and his
ascension into heaven were events either intrin
sically incredible in their nature or not. If the
former, the prevalent belief in them can only be
accounted for by miracles ; if the latter, they
ought to be believed even without miracles. St.
Aug. De Civ. Dei, xxii. 8.
(40) Only contented people are wise. Therefore the
tramp contented in his rags is necessarily a wise
man.
(41) Four-legged things are brutes.
Tables are four- legged things.
.*. Tables are brutes.
(42) The apparent volcanoes in the moon are not vol
canoes ; for eruptions are produced by gases only,
and there are no gases in the moon.
(43) To read the Scriptures is our duty. Therefore the
Captain was wrong in punishing the helmsman
for reading the Bible at the time when the ship
struck.
(44) The divine law orders that kings should be
honoured.
Louis Quatorze is a king.
/. The divine law orders that Louis Quatorze should
be honoured.
(45) Those who desire the same object are unanimous.
Caesar and Pompey both desire the same object,
namely, supreme power.
.'. They are unanimous.
(46) Either the ministers left at home will be ciphers or
EXERCISES.
they will not be ciphers. If they are ciphers,
cabinet government, which is equivalent to con
stitutional government, will receive a rude blow.
If they are not ciphers, the cabinet will be con
sidering matters of the utmost importance in the
absence, and the gratuitous absence, of two of its
most important members. ( The Standard,' Wed.
June 5, 1878.
(47) One patent stove saves half the ordinary amount
of fuel. Therefore two would save it all.
(48) One number must win in the lottery.
My ticket is one number.
.'. It must win.
(49) All good shepherds are prepared to lay down their
lives for the sheep.
Few in this age are so prepared.
.*. Few in this age are good shepherds.
(50) You cannot define the sun : for a definition must
be clearer than the thing defined, and nothing
can be clearer than the source of all light.
(51) To give the monopoly of the home market to the
produce of domestic industry . . . must in almost
all cases be either a useless or a hurtful regula
tion. If the produce of domestic can be brought
there as cheap as that of foreign industry, the
regulation is evidently useless ; if it cannot, it
is generally hurtful. Adam Smith, Wealth of
Nations, Bk. iv. ch. 2.
(52) Verberare est actio.
Ergo et vapulare.
(53) The ages of all the members of this family are
over 150.
The baby is a member of this family.
.'. Its age is over 150.
EXERCISES. 349
(54) Romulus must be an historical person ; because
it is not at all likely that the Romans, whose
memory was only burdened with seven kings,
should have forgotten the most famous of them,
namely, the first.
(55) All scientific treatises that are clear and true de
serve attention.
Few scientific treatises are clear and true.
/. Few scientific treatises deserve attention.
(56) The Conservative Government is an expensive
one ; for, on their going out of office, there was
a deficit.
(57) A man is forbidden to marry his brother's wife, or,
in other words, a woman is forbidden to marry
her husband's brother, that is, a woman is directly
forbidden to marry two brothers. Therefore a
man may not marry two sisters, so that a man
may not marry his wife's sister.
INDEX.
The references refer to the sections.
Abstraction, 97.
Acategorematic words, 71.
Accent, Fallacy of, 855.
Accident, 318.
Accident, Fallacy of, 860.
A dicto secundum quid, Fallacy
of, 86 1.
Amphiboly, Fallacy of, 848.
Antecedent
of a complex proposition, 212.
of an inference, 428.
A posteriori Truth, 232.
A priori Truth, 231.
' A ' Propositions, 260.
conversion of, 489.
Arguing in a circle, 882.
Argumentum ad hominem, etc.,
867.
Art, 20.
Attribute, 81 sqq.
Essential and non-essential,
320.
Attributives, 88 sqq.
Basis of Division, 391.
Categorematic words, 71.
Circulus in definiendo, 382.
Common Terms, 105.
how formed, 99.
nature of, 48.
Complex Proposition, 209.
conversion of, 709.
conversion by contraposition
of, 728.
conversion by negation of,
721.
divided into conjunctive and
disjunctive, 214.
permutation of, 718.
Complex Syllogism, 731.
mixed form of, 778.
Composition, Fallacy of, 849.
Concept, 36, 40 sqq.
Conception, 33.
Conceptualists, 51.
Conclusion, 540.
predicate of, 542.
subject of, 542.
Conjunctive Syllogisms, 733.
canon of, 742.
reduction of partly, 744.
partly conjunctive syllogisms
as an immediate inference,
753-
Connotation of Terms, 148.
352
INDEX.
Consequent of a complex propo
sition, 213.
of an inference, 428.
Consequent, Fallacy of, 873.
Contingent, 17.
Contradiction, Law of, 25 sqq.
Contradictory Propositions, 458.
Terms, 129.
Contrary Propositions, 458.
Terms, 130.
Converse, 480.
Conversion, 479.
of complex propositions, 709.
by contraposition, 516.
illative, 481.
by negation, 504.
per accidens, 487.
simple, 486.
rules of, 482.
Convertend, 480.
Copula, 58, 64, 186 sqq.
modality of, 196.
Correlatives, 142.
Deduction and Induction, differ
ence of, 431 sqq.
Deductive Inference, 442.
Deductive Logic, definition of,
4;
Definition of Terms, 347 sqq.
of Aristotle (6/>t<r/tos), 336.
final, 374.
nominal, 375.
provisional, 374.
real, 375.
rules of, 378.
Denotation of Terms, 152.
Description, 360.
Designations, 112.
Determination, 167.
Dictum de omni et nullo,
569-
de diverso, 641.
de exemplo et excepto, 642.
Difference, 318, 358.
generic, 410.
specific, 409.
Dilemma, 732, 779.
rebutted, 792.
reduction of, 796.
regarded as an immediate in
ference, 798.
Disjunctive Syllogism, 760.
canon of, 765.
reduction of, 766.
regarded as an immediate in
ference, 770.
Distinction, 424.
Distribution of Terms, 274.
four rules for, 293.
Divided whole, 393.
Dividing members, 394.
Division, 385 sqq.
by dichotomy, 41 2.
rules of, 395.
Division, Fallacy of, 851.
Division of Propositions, 206.
of terms, 86.
of things, 77.
Enthymeme,incorrectly so-called ,
557-
Enumeration, 387, 422.
Epicheirema, 803.
Episyllogism, 802.
' E ' Propositions, 260.
conversion of, 490.
Equivocation, Fallacy of, 845.
Excluded Middle, Law of, 25
sqq., 502.
INDEX.
353
Extension of Terms, 149 sqq.,
1 66 sqq.
Fallacy, 827 sqq.
of ambiguity, 831.
definition of, 828.
formal, 838.
logical, 836.
material, 831, 836.
of undisturbed middle, 585.
Figure of Speech, Fallacy of, 857.
Figures, of a Syllogism, 558.
special canons of, 633.
special rules of, 606.
special uses of, 648.
Formal Logic, 16.
Four Terms, Fallacy of, 840.
Fundamentum Divisionis, 391.
Generalisation, 168.
Genus, 318.
as used by Aristotle, 336.
cognate, 408.
proximate, 420.
subaltern, 406.
summum, 167, 404.
Heads of Predicables, 313.
as given by Aristotle, 336.
'Ideas' of Plato, 52.
Identity, Law of, 25 sqq.
Ignoratio Elenchi, Fallacy of,
865.
Ignotum per ignotius, 383.
Illicit Process, Fallacy of, 586.
Immediate Inference, 442 sqq.
by added determinants, 535.
by complex conception, 537.
applied to complex proposi
tions, 701.
Immediate Inference, compound
forms of, 503.
partly conjunctive syllogisms
regarded as, 753.
by conversion, 479.
disjunctive syllogisms regard
ed as, 770.
by opposition^ 462.
by permutation, 496.
Induction, differing from Deduc
tion, 430 sqq.
Inductive Logic, 2, 204.
' Inference,' various meanings of,
32, 36, 38.
Inferences in general, 426.
classification of, 441.
deductive, 442.
inductive, 430.
Infimae species, 405.
Intension of Terms, 150, 166.
Intuition, 232.
Inverse Variation, Law of, 1 66.
' I ' Propositions, 260.
conversion of, 490.
'Judgement,' various meanings
of, 32, 36.
' Law/ ambiguities of the word,
7 sqq.
Major Premiss, 544.
Major Term, 542.
Many Questions, Fallacy of, 884.
Mediate Inferences or Syllo
gisms, 444, 540 sqq.
axioms of, 576.
Membra Dividentia, 394.
Middle Term, 541.
position of, in a syllogism, 563.
A a
354
INDEX.
Minor Premiss, 545.
Minor Term, 542.
Modality, Question of, 196.
Mode, the, 196.
Moods of a Syllogism, 558.
determination of the legiti
mate, 599.
subaltern, 628.
valid in the Four Figures, 621.
mnemonics of, valid in Four
Figures, 629.
Name, definition of, 6r.
Negative Premisses and Conclu
sion, Fallacy of, 842.
Nominalists, 50, 54.
Non causa pro causa, Fallacy of,
883.
Nouns, 62.
Opposition, 449 sqq.
contradictory, 457.
contrary, 454.
laws of, 464.
subaltern, 456.
sub-contrary, 455.
' O ' Propositions, 260.
conversion of, 491.
Partition, 423.
Permutation, 496 sqq.
of Complex Propositions, 718.
Petitio Principii, Fallacy of, 874.
Predicable, 314.
Predicate of a Proposition, 58,
184.
read in extension, 307.
quantification of, 295 sqq.
quantity of, 281, 494.
Predication, 194.
in quid or in quale, 332.
Premisses, 540.
major, 544.
minor, 545.
Primary Existences, 55.
Problema, the, 556.
Proper Names, 113.
Property, 318.
generic, 411.
specific, 411.
Proposition, 172 sqq.
accidental, 238.
affirmative, 258.
complex or conditional, 209.
conjunctive or hypothetical,
214, 704.
conversion of, 479-
definition of, 178.
disjunctive, 214.
divisions of, 206.
essential, 238.
exceptive, 270.
exclusive, 266.
extensive, 264.
general, 251.
indefinite, 244.
intensive, 264.
modal, 205.
negative, 258.
particular, 240.
pure, 205.
quality of, 258.
quantity of, 246.
real or synthetical, 227.
simple or categorical, 207.
singular, 250.
tautologous or identical, 273.
universal, 239.
verbal or analytical, 224.
Proprium, 336.
/ NDEX.
355
Pro-syllogism, 802.
Quaestio, the, 556.
Quality, a, 82.
Quality of the matter, 204.
of propositions, 258.
Quantification of the Predicate,
295 sqq., 493.
Quantity of propositions, 258.
of terms, 148.
Realists, 49.
Real Kinds, 371.
Reasoning or Inference, 35.
the canon of, 569.
trains of, 800.
Reduction of propositions, 667.
of the dilemma, 796.
of disjunctive syllogisms, 766.
indirect, 691.
mnemonics for, 697.
by negation, 686.
ostensive or direct, 673.
of partly conjunctive syllo
gisms, 744.
Relation, a, 83, 144.
Relation, immediate inference
by, 462.
compatible and incompatible,
462.
Science, 20.
Secondary Existences, 55.
Simple Apprehension, 33.
Sorites, the, 807 sqq.
Specialisation, 167.
Species, 318.
cognate, 407.
infimae, 405.
subaltern, 406.
Subalternant, 458.
Subalternate, 458.
Subalternation, 458.
Subalterns, 458.
Sub-contraries, 458.
Sub-division, 401.
Subject, 58, 183.
how used, 264.
quantity of, 279.
Substance, 80, 84.
Sutnmum Genus, 167, 404.
Suppositio Materialis, 76.
Syllogism, 546 sqq.
complex, 731.
in common discourse, 557.
conjunctive, 733.
definition of, 552.
disjunctive, 760.
general rules of, 582.
figures of, 560, 563.
with three figures, 656.
legitimate moods of, 599 sqq.
mnemonics for, 598.
moods of, 559, 562.
Syncategorematic words, 70.
Synonym, 345.
Term, 57 sqq.
absolute, 140.
abstract, 95.
analogous, 139.
attributive, 88.
collective, 118.
common, 105.
concrete, 96.
connotative, 147.
contradictory, 129.
contrary, 130.
definition of, 347.
A a 2
356
INDEX.
Terms, distribution of, 275.
distributive and collective use
of, 119.
division of, 86.
equivocal, 137.
incompatible, 135.
individual, 121.
major, middle, and minor, 542.
negative, 126.
non-connotative, 147.
positive, 126.
privative, 126.
quantity of, 148.
Terms, relative, 141.
repugnant, 135.
singular, 43, 104.
subject, 87.
undistributed, 277.
univocal, 137.
Universals, nature of, 48, 55.
' U ' Propositions, 297.
Verb, 64.
Words, their relation to terms,
65 sqq.
THE END.
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Opinions of the Press.
' Mr. St. George Stock, an accomplished Oxonian, who believes, though
not without having found many cases of imposture, in those manifesta
tions of invisible agents which are classed generally under the head of
modern Spiritualism, has just published a book, called "Attempts at
Truth," which invents for sceptics a new horror, a horror such as the
scepticism of ancient times hardly ever conceived. .....'
The Spectator, Dec. 2, 1882.
'When "Two Brothers" published their "Guesses at Truth," and
thereby indirectly founded the great publishing house of Macmillan,
the plan of republishing magazine articles had scarcely come into
vogue. Whether or not this plan, now so universal, is a gain to society
we will not pause to consider. One thing is clear ; for an essay to get
published in a magazine it must, generally speaking, reach a level of
excellence which (as critics know to their sorrow) not all new books
attain to. And Mr. St. George Stock's " Attempts at Truth " (Trlibner)
are far above the average of " padding." He quite needlessly depre
cates the notion of having borrowed from Mr. Herbert Spencer; the
ideas which he works out (as well as his way of working) are in the air,
and are therefore the common property of every thinker ; and when
scientists like Mr. Wallace go in for Spiritualism Mr. Stock needs no
apology for endeavouring to point out the difference between the impos
ture (of which he says he has had abundant experience) and the
mysterious something which he believes to be real. He is happy in his
OPINIONS OF THE PRESS.
phrases, as where he calls Arthur Hallam the " Marcellus of Modern
Literature;" scarcely so happy when he calls Swedenborg the " Colum
bus of the world of mind ; " and if few will agree with such trenchant
assertions as " Natural theology is hopelessly gone if we give up the
revelation," they are useful because they force us to shake off for a
moment the shroud of commonplace which enwraps us. But in spite of
all Mr. Stock's reasoning we think Spiritualism will never stand against
the Materialism for which he looks on it as a substitute.'
The Graphic, Feb. 10, 1883.
* This is, at least in part, a republication of essays which have
appeared in the Westminster and Theological Reviews, and may, there
fore, be already known to some of our readers, but even to these the
essays will be welcome in their present form, as, although written at
different times, and under different conditions, they bear, as the writer
himself expresses it, " an organic unity " which cannot fail to place the
reader in a better position for mastering the subject than they could
possibly do when in the form of stray papers in different magazines.
Carefully thought out, clearly and logically argued, full of terse phrase
ology and telling imagery, these essays cannot fail, not only to be greatly
interesting, but also to lead those who pursue them to think out many
so-called problems for themselves, and even those who cannot acquiesce
in the writer's views must be quite willing to acknowledge his ability as
a thoughtful and conscientious writer.'
Public Opinion, Jan. 27, 1883.
' The destructive side of Mr. Stock's essays is more in keeping with
the bent of his mind, and those whose business it is to study writings of
the kind will find that he often turns his weapons against other forms of
scepticism than his own, and criticises them shrewdly enough ; though
his attempts at truth itself end only in failures.'
The Literary Churchman, Feb. 2, 1883.
' Anyone, then, who comes forward to challenge the exhaustiveness of
the rival theses which present themselves to our understanding on any
subject ought to be welcome, always supposing that he knows what he
is talking ab^out, and can state his case in intelligible language. These
conditions are ceitainly fulfilled by a writer who calls himself St. George
Stock, who has undertaken a task compared with which that of the
original owner of his prenom was a mere trifle.'
The National Reformer, May 13, 1883.
OPINIONS OF THE PRESS. 3
' " Attempts at Truth " (Triibner & Co.) is a collection of essays
contributed by Mr. St. George Stock to the Westminster Review and
other periodicals. The author has done well in bringing these essays
together in a compendious form, for they exhibit a clearness of thought
and expression and an impartiality of judgment, which bespeak for the
writer an analytical yet comprehensive mind.'
The Secular Review, Dec. 9, 1882.
' The essays in this very thoughtful book have, for the most part,
appeared before as review articles. They are on such permanently
important topics as " What is right ?" " Hume on Miracles," " Positive
view of Spiritualism and the Philosophy of Force," " Theism," " What
is Reality?" " Berkeley and Positivism," "Where is Heaven?" The
remarkable article on " Theism " -is from the Westminster Review, and
attracted a considerable amount of attention at the time of its publica
tion. Mr. Stock, in this volume, is everywhere Scholarly, independent,
keen, instructive.' The Truthseeker, June, 1883.
' As far as may be, we have allowed Mr. Stock to speak for himself.
The reader will find him worth the hearing. We may not always agree
in what he says, but we cannot but admire the way in which he says it.
Indeed, it would be hard to decide whether most to praise in our author
the clearness of the reasoning, or the singular felicity of the style. There
is no obscure argument, and hardly a slip-shod sentence, throughout the
book. Enough has been said here to show that there is much in the
book that is fruitful and suggestive ; much also that is of permanent
value. May it have as many readers as it deserves.'
The Psychological Review, December, 1882.
' An adequate review of these treatises would carry us too deeply and
extensively into the subjects comprised in them. Nor would it be easy
to condense an author who has himself the merit of condensing and
bringing to a logical focus most of the controversies he deals with.
Mr. St. George Stock is nearly always on the highest level of the argu
ment, which he answers, or states, at its best, and in its latest recognised
development. His analysis is invariably intelligible, and usually com
plete, and now and then we have to thank him for striking contributions
of original thought. And nowhere do we find the results of modern
speculation in several important departments set forth with more succinct
clearness, or in a more agreeable literary style.'
Light, March 3, 1883.
OPINIONS OF THE PRESS.
1 "Attempts at Truth," by St. George Stock. London, Triibner & Co.,
pp. 248. — This volume consists of sixteen thoughtful, interesting and
striking essays, which deal with some of the profoundest problems of
the day, such as right, reality, moral obligation, theism and spiritualism.
The latter subject is discussed with great fulness, generous candour, and
argumentative skill. The author is familiar with the whole literature of
his subject, he has quite a talent for this line of investigation — he has
marked powers of reasoning, and a graceful, telling, persuasive, literary
style. The subjects are discussed in a calm, courteous and philosophical
spirit, and the work altogether is both interesting and fresh, instructive,
and thought provoking. It is a most valuable and welcome contribution
to our current controversies. The author is a fearless thinker, a skilful
dialectician, and a charming writer ; hence this volume ought to have a
wide circulation.' The Battley News, Feb. 6, 1886.
' " LesTentatives vers la verite," par Georges Stock (Londres, Triibner),
sont une ceuvre, comme notre epoque en voit eclore malheureusement
un si grand nombre, une ceuvre d'agnostique, suivant le vocabulaire
anglais, et de positiviste suivant le vocabulaire fran9ais. M. Stock
s'efforce de laver son ecole de 1'accusation de detruire la morale
commune et d'etre impuissante a en fonder une nouvelle.'
Bibliographic Catholique, Paris, July, 1883.
' Here at last has arisen in Oxford a philosopher who has something
fresh to say, and says it in a tongue understanded of the people. . . . Alone,
or nearly alone, among men who have speculated upon fundamentals
from under Alma Mater's shadow, Mr. St. George Stock looks not back
but forwards. Academic models have tinged his shape rather than his
substance, and academic paralysis of the soul's free play has not touched
him.' Oxford Magazine, Jan. 24, 1883.
' Before coming together in book form, most of these essays made
their appearance in various periodicals. They are certainly most read
able, and five years of companionship with the world have not made
them in any way stale. The author does not seek to win favour by
always getting on the popular side of questions. For instance, he
attaches importance to spiritualism, and gives a. degree of credit to its
phenomena.' The Cosmopolitan, Jan. 1888.
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THE NICOMACHEAN ETHICS
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BOOKS I-IV (OMITTING I, 6) AND X, 6-9.
TRANSLATED WITH A CATECHETICAL ANALYSIS.
OXFORD : B. H. BLACKWELL ; LONDON : SIMPKIN, MARSHALL
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Opinions of the Press.
' The new translator may be congratulated upon his Summaries, upon
a very suggestive Catechetical Analysis, and upon some minor ingenious
devices for assisting the eye, as for instance the putting all Aristotle's
digressions into brackets. The translation has kept clear of error in all
the hard test-passages where we have consulted it ; but it sometimes
misses the full bearing of the Greek in easier passages. Thus let us
examine a single chapter But there are not many chapters
in which we should have to dissent so often from Mr. Stock, and we can
confidently recommend his book to Passmen.'
The Oxford Magazine, May 26, 1886.
' This is a translation of those parts of the Ethics which are taken in
for examination by the Oxford Passman. To each book is prefixed
a brief summary of its contents, and at the end of the whole is placed
a series of very minute questions, covering not only every chapter but
every section, and designed to bring out every point in Aristotle's argu
ment, sometimes even to suggest reflexion upon it. This "catechetical
analysis " is intended especially to help those who are trying to get up
OPINIONS OF THE PRESS.
their work by themselves, and it seems very well calculated to do so.
Of the translation, which Mr. Stock acknowledges to be meant for
" the less ambitious student," I should say that it is literal enough for
the least ambitious and that, so far as I have tested it, it seems accurate.'
H. RICHARDS, The Classical Review, June, 1887.
' By some accident, which we cannot precisely explain, we omitted to
review this book in its due turn last year. Its soundness and utility
are now sufficiently recognised, and it is rather by way of apology than
for any other reason, that we propose to say a few words on it at the
eleventh hour. The book consists of a translation of those parts of the
Ethics which are read for Pass Finals, together with an introductory
summary to each book, and a Catechetical Analysis at the end of the
volume. The translation unites in a striking degree the qualities of
closeness, conciseness, and elegance. It is, perhaps, hardly intended for
English readers, and is, therefore, all the more suitable for Oxford.
Here and there it would be possible to question the renderings of diffi
cult passages ; this, in fact, has been done, and is inevitable ; it is no
reproach to the book, which is recommended none the less by those
who thus occasionally criticise it. The summaries strike us as written
with great clearness, unusual power of condensation, and a precision
and happiness of language which entitle them to praise even on the
ground of literary style. A glance at these summaries would itself
'convince us that the author had well studied his subject. Finally, the
long series of questions at the end constitutes, in point of fact, a close
analysis of the entire work, and is extremely well suited to assist be
ginners, or (as Mr. Stock suggests) solitary students. This Catechetical
Analysis is, on the whole, the prominent feature of the volume before
us. Students will find it very useful in gradually accustoming them to
understand the bearing of the questions which are set in the schools.
Mr. Stock's careful scholarship and his experience in tuition are no
secret in Oxford. Our confidence in his book is increased by his ex
planation that he has twice attended Professor Chandler's course of
lectures on the subject, lectures so replete with wit and independence,
profundity and breadth. We may be allowed to point out that on
page 92, in the I3th line of the summary, we observe the word latter,
where former is obviously meant.'
The Oxford Review, Nov. 9, 1887.
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THE MENO OF PLATO.
WITH INTRODUCTION AND NOTES.
CLARENDON PRESS SERIES, 1887.
Opinions of the Press.
' This excellent edition of the Meno will supply a felt want, and
Mr. St. George Stock has earned a deep debt of gratitude from every
classical student for the labour he has expended, and the minute
scholarship he has brought to bear upon the work. To do justice in
a review of this work would require far more space than can be given in
our columns, and all we can do is simply to say that the Introduction —
a most elaborate one, not only to the present work, but to Plato's
writings in general — the Analysis of the Argument, and the Notes,
which clear away all difficulties, and give all necessary aids for the
explication of the substance and style of the dialogue, are all that could
be desired. How clear, among many others equally so, is the distinction
on p. 27 on the phrase, dp' orav TOVTO XeyojfAfv, rude \eyonev, between
TOVTO and roSe, although in a passage in Herodotus IX the rule does
not hold good. And, as a proof of the carefulness of the editing in a
different way, we may refer to the note on p. 29 on Protagoras. The
Text and Notes are printed separately — an arrangement which, edu
cationally and otherwise, meets with our hearty approval. Mr. St.
George Stock has done his work well, and the opinion we have given of
the book is without the slightest reservation.'
The Schoolmaster, Sept. 3, 1887.
OPINIONS OF THE PRESS.
' In the Meno the chief fault we have to find is the occasional omis
sion of notes where needed.' The Classical Review, Feb. 1888.
' The text is K. F. Hermann's, and the commentary is carefully
compiled.' Athenaum, Dec. 31, 1887.
' His obligations to the patient and laborious Germans, who seem to
have forestalled their English cousins in every department of critical
analysis, are acknowledged in fitting terms, and a masterly introduction,
or rather treatise, on the philosophy known as Platonic furnishes all the
information necessary to the student, while the somewhat vexed and
abstruse questions of order, date, and authenticity are considerately
relegated in favour of more purely technical points.'
71ie Week, Toronto, Oct. 2, 1887.
Extra f cap. 8vo., price 2s. 6d.
THE APOLOGY OF PLATO.
WITH INTRODUCTION AND NOTES.
CLARENDON PRESS SERIES, 1887.
Opinions of the Press.
1 " The world," says Mr. Stock, " will always be the better for the
Apology of Socrates " ; and we heartily agree with him. But it is
necessary to make it accessible to the modern world ; and Mr. Stock
has gone manfully to work with introduction, running analysis and
notes. The introduction wins for the hero the sympathy of the reader
before he comes to Socrates' own words. It sets forth what little is
known of the man, describes his surroundings, and does as much, per
haps, as can be done to explain the standing wonder of his judicial
murder. About the notes we have no complaint except that we should
like a few more of them.' The Academy, Feb. 1 1, 1888.
' All that need be said of this production is, it is like the Clarendon
Press publications, more especially clerical books, admirable.'
Belfast Morning News, Oct. 26, 1887.
' Mr. Stock has done his work well, the introduction being especially
valuable.' Practical Teacher.
' Mr. Stock, in his lucid and learned introduction, has certainly
struck the key-note when he tells us that " the world will always be the
better for the Apology of Socrates " Of the notes we must
10 OPINIONS OF THE PRESS.
speak in very high terms. They are ample, and with very rare excep
tions they meet every difficulty with all the necessary help. In this
respect they are by far the most serviceable notes yet published in any
Knglish edition of Plato's Apology.' School Board Chronicle.
' Mr. Stock's notes have no interest for the Scholar, unless it be the
interest of detecting occasional mistakes.'
Oxford Magazine, March 7, 1888.
' The introduction is, on the whole, worthy of this be
ginning. It is diffuse, high-flown, and in thoroughly bad taste. Nor
are the notes satisfactory ...... Aspasia is referred to with equal
grace and originality as " a Socrates in petticoats." Mr. Stock's notes
are, for the most part, correct enough, and perhaps in much that he has
written he was deliberately writing down to boys ; but we can assure
him that boys are quite capable of distinguishing between sound sense
and mere " high-falutin," also between the humourist and the buffoon.'
The Journal of Education, March 1, 1888.
' These are pleasant handy editions with text and notes in separate
volumes according to the convenient modern plan. The editor writes
easily and well, and the notes are useful and generally correct.'
The Classical Review, Feb. 1888.
' Mr. Stock's work is not free from blemishes, but occasionally rises
above mediocrity.' Athenaum, Nov. 3, 1888.
' The Apology is in two volumes. It is edited by St. George Stock,
M.A. In the first are contained the introduction and the text ; in the
second the notes. Both are characterized, not only by scholarship, but
by what is of even more importance to those for whom the work is
intended, a keen appreciation of the difficulties of the student, and an
admirable effort to smooth them away.'
Cork Examiner, Oct. 20, 1887.
' This issue will be found useful for senior Greek students. The text
followed is that of K. F. Hermann, and the notes contain many valu
able references.' Northern Whig, Belfast, Dec. 7, 1887.
•' This is an admirable edition of Plato's defence of the character and
life of his master and teacher, whom the fickle Athenians condemned to
OPINIONS OF THE PRESS. II
drink the fatal hemlock. It is uniform with the same editor's edition
of the " Meno," and having regard to the rigorous care with which the
text has been printed, the excellence of the arrangement of the defence
under analytical sub-heads, the fulness and order of the introduction,
and the sound scholarship displayed in the notes, there need be no
hesitation in recommending it for use in intermediate schools, and
even in the higher classes of colleges. The Platonic idioms are clearly
and logically explained, and the historical notes leave nothing to be
desired.' Freemaris Journal, Dublin, Oct. 21, 1887.
' The editing of this well-known portion of Plato must have been
a labour of love with Mr. Stock, so thoroughly and efficiently has he
executed his share of the work. The introduction is excellent, and
deserves to occupy a much higher place than in an edition which the
author modestly characterises as " of a somewhat elementary character.''
It extends to about twenty-eight pages, and, did space permit, we would
have been desirous of giving some quotations from its eloquent pages.
Running commentaries precede the different sections of the work, a
valuable aid to the consecutive reasoning of the work itself. The notes
are very full, embracing all historical, biographical, and grammatical
allusions. The last-named are exceedingly minute, and leave no dif-
culty unsolved, and wherever an alternative reading or translation is
possible, that is invariably given. We had marked several passages as
examples of careful editing, but these became so numerous that we
prefer simply to say, as the result of our examination of them, that they
bear ample testimony to the high scholarship and professional expe
rience of Mr. Stock. A better edition (elementary, as Mr. Stock will
have it) could not be placed in the hands of students.'
Schoolmaster ; Jan. 21, 1888.
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A Glimpse of the World.
Katharine Ashton.
Laneton Parsonage.
Margaret Percival. Ursula.
Stevenson's (B. L.) The Dynamiter. Fcp. 8vo. Is. sewed ; 1*. Qd. cloth.
— — Strange Case of Dr. Jekyll and Mr. Hyde. Fcp. 8vo. 1*.
sewed ; 1*. Qd. cloth.
Trollope's (Anthony) Novels. Fcp. 8vo. 1*. each, boards ; 1*. 6d. cloth.
The Warden | Barchester Towers.
POETRY AND THE DRAMA.
Armstrong's (Ed. J.) Poetical Works. Fcp. Svo. 5s.
— (G. F.) Poetical Works :—
Poems, Lyrical and Dramatic. Fcp.
Svo. 6*.
Ugone : a Tragedy. Fcp. Svo. 6*.
A Garland from Greece. Fcp. 8vo.9*.
King Saul. Fcp. Svo. 5*.
King David. Fcp. Svo. 6*.
Stories of Wicklow. Fcp. Svo. 9*.
Mephittopheles in Broadcloth: a
Satire. Fcp. Svo. 4s.
Victoria Regina et Imperatrix : a
Jubilee Song from Ireland, 1887.
4to. 2s. Qd.
King Solomon. Fcp. Svo. 6s.
Ballads of Berks. Edited by Andrew Lang. Fcp. Svo. 6*.
Bowen's Farrow Songs and other Verses. Fcp. Svo. 2*. 6d. ; or printed on
hand-made paper, 5*.
Bowdler's Family Shakespeare. Medium Svo. 14*. 6 vols. fcp. Svo. 21*.
Dante's Divine Comedy, translated by James Innes Mincbin. Crown Svo. 15*,
Goethe's Faust, translated by Birds. Large crown Svo. 12s. Qd.
— — translated by Webb. Svo. 12*. Qd.
— — edited by Selss. Crown Svo. 5s.
Ingelow's Poems. 2 Vols. fcp. Svo. 12*. ; Vol. 3, fcp. Svo. 5s.
— Lyrical and other Poems. Fcp. Svo. 2*. Qd. cloth, plain ; 3*. cloth,
gilt edges.
Kendall's (Mrs.) Dreams to SelL Fcp. Svo. 6s.
Macaulay's Lays of Ancient Rome. Illustrated by Scharf. 4to. 10*. 6d.
Popular Edition, fcp. 4to. Gd. swd., 1*. cloth.
— Lays of Ancient Rome, with Ivry and the Armada. Illustrated by
Weguelin. Crown Svo. 3*. Qd. gilt edges.
Nesbit's Lays and Legends. Crown Svo. 5*.
Newman's The Dream of Gerontius. 16mo. Qd. sewed ; Is. cloth.
— Verses on Various Occasions. Fcp. Sro. 6*.
Reader's Voices from Flowerland, a Birthday Book, 2*. Qd. cloth, 3*. Gd. roan.
Southey's Poetical Works. Medium 8vo. 14*.
Stevenson's A Child's Garden of Verses. Fcp. Svo. 5*.
Virgil's JEneid, translated by Conington. Crown Svo. 9*.
— Poems, translated into English Prose. Crown Svo. 9*.
AGRICULTURE, HORSES, DOGS, AND CATTLE.
Fitzwygram's Horses and Stables. Svo. 5*.
Lloyd's The Science of Agriculture. Svo. 12*.
Loudon's Encyclopaedia of Agriculture. 21*.
Prothero's Pioneers and Progress of English Farming. Crown Svo. 5*.
Steel's Diseases of the Ox, a Manual of Bovine Pathology. Svo. 15*.
— — — Dog. Svo. 10*. Qd.
LONGMANS, GKEEN, & CO., London and New York.
12 General Lists of Works.
Stonehenge's Dog in Health and Disease. Square crown 8vo. 7*. M.
— Greyhound. Square crown 8vo. 15*.
Taylor's Agricultural Note Book. Fcp. 8vo. 2s. Gd.
Ville on Artificial Manures, by Crookes. 8vo. 21«.
Youatt's Work on the Dog. 8vo. 8*.
— — — — Horse. 8vo. 7*. 6<J.
SPORTS AND PASTIMES.
The Badminton Library of Sports and Pastimes. Edited by the Duke of Beaufort
Mid A, B. T. Watson. With numerous Illustrations. Cr. 8vo. 10*. Gd. each.
Hunting, by the Duke of Beaufort, <fec.
Fishing, by H, Chohnondeley-Pennell, &c. 2 vols.
Racing, by the Earl of Suffolk, &c.
Shooting, by Lord Walsingham, &c. 2 vols.
Cycling. By Viscount Bury.
Athletics and Football. By Montague Shearman, &c.
Boating. By W. B. Woodgate, &c.
Cricket. By A. G. Steel, &c.
Driving. Ey the Duke of Beaufort, &c.
*«* Other Volumes in preparation,
Campbell-Walker's Correct Card, or How to Play at Whist. Pep. 8vo. 2s. Gd.
Ford's Theory and Practice of Archery, revised by W. Butt. 8vo. 14*.
Francis's Treatise on Fishing in all its Branches. Post 8vo. 15*.
Longman's Chess Openings. Fcp. 8vo. 2*. Gd.
Pease's The Cleveland Hounds as a Trencher-Fed Pack. Royal 8vo. 18*.
Pole's Theory of the Modern Scientific Game of Whist. Fcp. 8vo. 2*. 6d.
Proctor's How to Play Whist. Crown 8vo. 5*.
Ronalds's Fly-Fisher's Entomology. 8vo. Us.
Wilcocks's Sea- Fisherman. Post 8vo. 6*.
ENCYCLOPAEDIAS, DICTIONARIES, AND BOOKS OF
REFERENCE.
Acton's Modern Cookery for Private Families. Fcp 8vo. 4*. Gd.
Ayre's Treasury of Bible Knowledge. Fcp. 8vo. 6*.
Cabinet Lawyer (The), a Popular Digest of the Laws of England. Fcp. 8vo. 9*.
Cates's Dictionary of General Biography. Medium 8vo. 28*.
Gwilt's Encyclopaedia of Architecture. 8vo. 52*. Gd.
Keith Johnston's Dictionary of Geography, or General Gazetteer. 8vo. 42*.
M'Culloch's Dictionary of Commerce and Commercial Navigation. 8vo. 63*.
Maunder's Biographical Treasury. Fcp. 8vo. 6*.
— Historical Treasury. Fcp. 8vo. 6*.
— Scientific and Literary Treasury. Fcp. 8vo. 6*.
— Treasury of Bible Knowledge, edited by Ayre. Fcp. 8vo. 6*.
— Treasury of Botany, edited by Lindley & Moore. Two Parts, 12*.
— Treasury of Geography. Fcp^ 8vo. 6*.
— Treasury of Knowledge and Library of Reference. Fcp. 8vo. 8*.
— Treasury of Natural History. Fcp. 8vo. 6*.
Quain's Dictionary of Medicine. Medium 8vo. 31*. Gd., or in 2 vols. 34*.
Reeve's Cookery and Housekeeping. Crown 8vo. 5*.
Rich's Dictionary of Roman and Greek Antiquities. Crown 8vo. 7*. Gd.
Roget's Thesaurus of English Words and Phrases. Crown 8vo. 10*. 6d.
Wiilich's Popular Tables, by Marriott. Crown 8vo. 10*. Gd.
WORKS BY MRS. DE SALIS.
Savouries a la Mode. Fcp. 8vo. 1*.
Entries a. la Mode. Fcp. 8vo. 1*. 6d.
Soups and Dressed Fith a la Mode.
Fcp. 8vo. 1*. Gd.
Sweets and Supper Dishes, & la Mode.
Fcp. 8vo. 1*. Gd.
Oytters a. la Mode. Fcp. 8vo. 1*. 6d.
Vegetables a la Mode. Fcp. 8vo. Is. Gd.
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A SELECTION
OP
EDUCATIONAL WORKS.
TEXT-BOOKS OF SCIENCE.
FULLY ILLUSTRATED.
Abney'a Treatiie on Photography. Fcp. 8vo. 3*. 64.
Anderson's Strength of Materials. 3s. 6d.
Armstrong's Organic Chemistry. 3*. 6<i.
Ball's Elementi of Astronomy. 6s.
Barry'i Bailway Appliances. 3s. 6d.
Bauennan'e Systematic Mineralogy. 6*.
— Descriptive Mineralogy. 6*.
Blozam and Huutington's Metals. 6j.
Glazebrook'i Physical Optics. 6*.
Glazebrook and Shaw's Practical Physics. 6*.
Gore's Art of Electro-Metallurgy. 6*.
Griffin's Algebra and Trigonometry. Zs. 6d. Notes and Solutions, 3j. 6d,
Holmes's The Steam Engine. 6*.
Jeukin's Electricity and Magnetism. 3i. 6d.
Maxwell's Theory of Heat. 3*. 6d.
Merrifield's Technical Arithmetic and Mensuration. 3*. 6d. Key, 3*. 64.
Miller's Inorganic Chemistry. 3*. 6d.
Preece and Sivewright's Telegraphy. St.
Kutley's Study of Kocks, a Text-Book of Petrology. 4*. 64.
Shelley's Workshop Appliances. 4*. 6d.
Thome's Structural and Physiological Botany. 6*.
Thorpe's Quantitative Chemical Analysis. 4». 64,
Thorpe and Muir's Qualitative Analysis. 3s. 64.
Tilden's Chemical Philosophy. 3*. 6<2. With Anaweri to Problems, it. 6<J.
Unwin's Elements of Machine Design. 6s.
Watson's Plane and Solid Geometry. 3t. Gd.
THE GREEK LANGUAGE.
Bloomfield's College and School Greek Testament. Fcp. 8vo. 5i.
Bolland & Lang's Politics of Aristotle. Post 8vo. 7s. 6d.
Collis's Chief Tenses of the Greek Irregular Verbs. 8vo. It.
— Pontes Greeci, Stepping-Stone to Greek Grammar. 12mo. 3*. 6<(.
— Praxis Grseca, Etymology. 12mo. 2s. 6d.
— Greek Verse-Book, Praxis lambica. 12mo. is. 6d.
Farrar's Brief Greek Syntax and Acoidence. 12mo. 4*. 6d.
— Greek Grammar Rules for Harrow School. 12mo. Is. Gd.
Geaxe's Notes on Thucydides. Book I. Fcp. 8vo. 2j. 6d.
LONGMANS, GREEN, & CO., London and New York.
14 A Selection of Educational Works.
Hewitt's Greek Examinatlon-Papers. 12mo. 1*. Gd.
Isbister's Xenophon's Anabasis, Books I. to III. with Notei. 12mo. 8j. 6d.
Kennedy's Greek Grammar. 12mo. 4*. Gd.
Liddell & Scott's English-Greek Lexicon. 4to. 36*. ; Square 12mo. 7s. 6d.
Mahaffy's Classical Greek Literature. Crown Svo. Poets, 7s. Gd. Prose Writers,
Is. Gd.
Morris's Greek Lessons. Square 18mo. Part I. 25. 6d. ; Part II. 1*.
Parry's Elementary Greek Grammar. 12mo. 3s. 6d.
Plato's Republic, Book I. Greek Text, English Notes by Hardy. Crown 8vo. 3*.
Sheppard and Evans's Notes on Thucydides. Crown 8vo. 7*. Gd.
Thucydides, Book IV. with Notes by Barton and Chavasse. Crown 8vo. 5s.
Valpy's Greek Delectus, improved by White. 12mo. 2*. Gd. Key, 25. Gd.
White's Xenophon's Expedition of Cyrus, with English Notes. 12mo. 7*. 6d.
WilMns's Manual of Greek Prose Composition. Crown Svo. 5s. Key, 5s.
— Exercises in Greek Prose Composition. Crown Svo. 4*. Gd. Key, 2s. Gd.
— New Greek Delectus. Crown Svo. 35. Gd. Key, 2s. Gd.
— - Progressive Greek Delectus. 12mo. 45. Key, 2s, 6d,
— Progressive Greek Anthology. 12me. 5s.
— Scriptores Attici, Excerpts with English Notes. Crown Svo. 7s. 6d.
— Speeches from Thucydides translated. Post Svo. 65.
Yongc's English-Greek Lexicon. 4to. 21*. ; Square 12mo. 8*. Gd.
THE LATIN LANGUAGE.
Bradley's Latin Prose Exercises. 12mo. 35. Bd. Key, 5s.
— Continuous Lessons in Latin Prose. 12mo. 55. Key, 5s. 6d.
— Cornelius Nepos, improved by White. 12mo. Ss. Gd.
— Eutropius, improved by White. 12mo. 25. Gd.
— Ovid's Metamorphoses, improved by White. 12mo. 4.?. Gd.
— Select Fables of Phaedrus, improved by White. 12mo. 2$. Gd,
Collis's Chief Tenses of Latin Irregular Verbs. Svo. 1*.
— Pontes Latini, Stepping-Stone to Latin Grammar. 12mo. 35. Gd.
Hewitt's Latin Examination-Papers. 12mo. 1*. Gd.
Isbister's Caesar, Books I.- VII. 12mo. 4s. ; or with Reading Lessons, 4». 6d.
— Caesar's Commentaries, Books I.-V. 12mo. 35. Gd.
— First Book of Caesar's Gallic War. 12mo. Is. Gd.
Jerram's Latine Reddenda. Crown Svo. 15. Gd.
Kennedy's Child's Latin Primer, or First Latin Lessons. 12mo. 2s,
— Child's Latin Accidence. 12mo. Is.
— Elementary Latin Grammar. 12mo. 85. Gd.
— Elementary Latin Reading Book, or Tirocinium Latinum. 12mo. 2s.
— Latin Prose, Palaestra Stili Latini. 12mo. 6*.
— Latin Vocabulary. 12mo. 25. Gd.
— Subsidia Primaria, Exercise Books to the Public School Latin Primer.
I. Accidence and Simple Construction, 25. Gd. II. Syntax, 3*. Gd.
— Key to the Exercises in Subsidia Primaria, Parts I. and^II. price 5s.
— Subsidia Primaria, III. the Latin Compound Sentence. 12mo. 1».
LONGMANS, GBEEN, & CO., London and New York.
A Selection of Educational Works.
15
Kennedy's Curriculum Still Latini. 12mo. 4*. 6d. Key, 7t. 6d.
— Palaestra Latins, or Second Latin Heading Book. 12mo. 6*.
Moody's Eton Latin Grammar. 12mo. 2s. Gd. The Accidence separately, It.
Morris's Elementa Latina. Fcp. 8vo. 1*. Gd. Key, 2s. Gd.
Parry's Origines Romanse, from Livy, with English Notea. Crown 8vo. 4*.
The Public School Latin Primer. 12mo. 2s. Gd.
— — — — Grammar, by Eev. Dr. Kennedy. Post 8vo. 7*. Qd.
Prendergast's Mastery Series, Manual of Latin. 12mo. 2*. Gd.
Rapier's Introduction to Composition of Latin Verse. 12mo. 3s. Gd. Key, 2s. 6d.
Bheppard and Turner's Aids to Classical Study. 12mo. 5s. Key, 6s.
Valpy's Latin Delectus, improved by White. 12mo. 2*. Gd. Key, 3*. Gd.
Virgil's ^Eneid, translated into English Verse by Conington. Crown 8vo. 9*.
— Works, edited by Kennedy. Crown 8vo. 10*. Gd.
— — translated into English Prose by Conington. Crown 8vo. 9s.
Walford'a Progressive Exercises in Latin Elegiac Verse. 12mo. 2s. Gd. Key, 5*.
White and Riddle's Large Latin-English Dictionary. 1 vol. 4to. 21*.
White's Concise Latin-Eng. Dictionary for University Students. Royal 8vo. 12*.
— Junior Students' Eng.-Lat. & Lat.-Eng. Dictionary. Square 12mo. 6*.
cPTinrfttp1v f The Latin-English Dictionary, price 3*.
weiy ^ The Englisn.Latin Dictionary, price 3*.
Tonge's Latin Gradus. Post 8vo. 9*. ; or with Appendix, 12*.
WHITE'S GRAMMAR-SCHOOL GREEK TEXTS.
.fflsop (Fables) & Palsephatus (Myths).
32 mo. 1*.
Euripides. Hecuba. 2*.
Homer, Iliad, Book I. 1*.
— Odyssey, Book I. 1*.
Lucian, Select Dialogues. 1*.
Xenophon,. Anabasis, Books I. III. IV.
V. & VI. Is. Gd. each : Book II. 1*. ;
Book VII. 2s.
Xenophon, Book I. without Vocabu
lary. 3d.
St. Matthew's and St. Luke's Gospels,
2s. fid. each.
St. Mark's and St. John's Gospels.
1*. Gd. each.
The Acts of the Apostles. 2f. Gd.
St. Paul's Epistle to the Romans. 1*. Gd.
The Four Gospels in Greek, with Greek-English Lexicon. Edited by John T.
White, D.D. Oxon. Square 32mo. price 5*.
WHITE'S GRAMMAR-SCHOOL LATIN TEXTS.
Cffisar, Gallic War, Books I. & IT. V.
& VI. 1*. each. Book I. without
Vocabulary, 3d.
Csesar, Gallic War, Books III. & IV.
9d. each.
Csesar, Gallic War, Book VII. Is. Gd.
Cicero, Cato Major (Old Age). 1*. Gd.
Cicero, Lselius (Friendship). 1*. Gd.
Eutropius, Roman History, Books I.
& II. 1*. Books III. & IV. 1*.
Horace,0des, Books I. II. & IV. 1*. each.
Horace, Odes, Book III. 1*. Gd.
Horace, Epodes and Carmen Seculare.
1*.
Nepos, Miltiades, Simon, Pausanias,
Aristides. 9d.
Ovid. Selections from Epistles and
Fasti. 1*.
Ovid, Select Myths from Metamor
phoses. 9d.
Phaedrus, Select Easy Fables,
Phsedrns, Fables, Books I. & II. 1*.
Sallust, Bellum Catilinarium. 1*. 6d.
Virgil, Georgics, Book IV. 1*.
Virgil, ^Sneid, Books I. to VI. 1*. each.
Book I. without Vocabulary, 3d.
Virgil, ^Eneid, Books VII. to XII.
It. Gd. each.
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16 A Selection of Educational Works.
THE FRENCH LANGUAGE.
Albites'a How to Speak French. Fcp. 8vo. 5s. Gd.
— Instantaneous French Exercises. Fcp. 2s. Key, 2s.
Cassal's French Genders. Crown 8vo. 3*. Gd.
Oassal & Karcher's Graduated French Translation Book. Part I. 3*. 6d.
Part II. 5s. Key to Part I. by Professor Cassal, price 5*.
Contanseau's Practical French and English Dictionary. Post 8vo. 3*. Cd.
— Pocket French and English Dictionary. Square 18mo. 1*. Gd.
— Premieres Lectures. 12mo. 2s. Gd.
— First Step in French. 12mo. 2s. Gd. Key, 3«.
— French Accidence. 12mo. 2s. Gd.
— Grammar. 12mo. 4s. Key, 3*.
Contanseau's Middle-Class French Course. Fcp. 8vo. :—
Accidence, Sd.
Pyntax, Sd.
French Conversation-Book, Bd.
First French Exercise-Book, Sd.
Second French Exercise- Book, 8d.
French Translation-Book, 8J,
Easy French Delectus, 8d.
First French Reader, Sd.
Second French Reader, Sd.
French and English Dialogues, Bd.
Contanseau's Guide to French Translation. 12mo. 3$. Gd. Key 3*. Gd.
— Prosateurs et Po6tes Francais. 12mo. 6*.
-- Precis de la Litterature Francaise. 12mo. 3*. Gd.
— Abreg6 de 1'Histoire de France. 12mo. 2s. Qd.
Feval's Chouans et Bleus, with Notes by C. Sankey, M.A. Fcp. 8ro. 2*. 6d.
Jerram's Sentences for Translation into French. Cr. 8vo. 1*. Key, 2s. 6d.
Prendergast's Mastery Series, French. 12mo. 2*. Gd.
Souvestre's Philosophe sous les Toits, by Stievenard. Square 18mo. 1*. 84.
Stepping -Stone to French Pronunciation. 18ino. 1*.
Stievenard's Lectures Francaises from Modern Authors. 12mo. 4*. 6d.
Rules and Exercises on the French Language. 12mo. 3s. 6d.
Tarver's Eton French Grammar. 12mo. Qs. 6d.
THE GERMAN LANGUAGE.
B'ackley'a Practical German and English Dictionary. Post 8vo. 3s. 6d.
Euchheim's German Poetry, for Repetition. 18mo. 1*. Gd.
Collis's Card of German Irregular Verbs. 8vo. 2s.
Fischer-Fischart's Elementary German Grammar. Fcp. 8vo. 2s. Gd.
Just's German Grammar. 12mo. 1*. 6d,
— German Reading Book. 12mo. 3s. 6d.
Longman's Pocket German and English Dictionary. Square 18mo. 2s. 6<t
Naftel's Elementary German Course for Public Schools. Fcp. 8vo.
German Accidence. 9d.
German Syntax. 9d.
First German Exercise-Book, 9d.
Second German Exercise- Book.
Prendergast's Mastery Series, German. 12mo. 2*. Gd.
Quick's Essentials of German. Crown 8vo. 3*. Gd.
Selss's School Edition of Goethe's Faust. Crown 8vo. 5*.
— Outline of German Literature. Crown 8vo. 4*. Gd.
Wirth'e German Chit-Chat. Crown 8vo. 2s. Gd.
German Prose Composition Book.
First German Reader. 9d.
Second German Reader. 9(2.
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